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【323442】2023九年级数学上册 第24章 解直角三角形检测题(含解析)(新版)华东师大版

时间:2025-01-16 18:35:06 作者: 字数:12485字
简介:


24章 解直角三角形检测题

(本检测题满分:120分,时间:120分钟)

一、选择题(每小题2分,共24分)

1.计算: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

A. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> B. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> C. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> D. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

2.在直角三角形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 中,已知 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> =( )

A. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> B. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> C. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> D. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

3.2013·浙江温州中考)如图,在 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 值是( )

A. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> B. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> C. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> D. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

4.如图,四边形ABCD是梯形,ADBCCA是∠BCD的平分线,且ABACAB=4AD=6,则tan B=( )

A.2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> B.2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> C. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> D. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

5.如图,Rt△ABC中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 90°,将△ABC折叠,使A点与BC的中点D重合,折痕为MN,则线段BN的长为( )

A. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> B. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> C.4 D.5

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>




3题图


5题图



6.在△ABC中,若三边BCCAAB满足 BCCAAB=51213cos B=( )

A. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> B. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> C. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> D. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

7.已知 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,F分别在射线AD,射线BC上,若点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 与点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 关于 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 对称,点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 与点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 关于 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 对称, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 相交于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,则( )

A. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> B. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

C. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> D. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>


组合 3337

组合 2616 7题图

8.河堤横断面如图所示,堤高BC=6 m,迎水坡AB的坡比为1∶ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,则AB的长为( )

A.12 m B.4 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> m C.5 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> m D.6 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> m

9.如图,一个小球由地面沿着坡度 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 的坡面向上前进了10 m,此时小球距离地面的高度为( ) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

A.5 m B.2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> m C.4 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> m D. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> m

10.如图,在菱形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 的值是( )

A <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> B2 C <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> D <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

组合 2626








11.已知直角三角形两直角边长之和为7,面积为6,则斜边长为(

A. 5 B.  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> C. 7 D.  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

12.如图,已知:45°A90°,则下列各式成立的是( )

A. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> B. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> C. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> D. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 、填空题(每小题3分,共18分)

13.比较大小: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> .(填“>”“=”或“<”)

14.如图,在△ABC中,∠BAC=30°AB=ACADBC边上的中线,∠ACE= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> BAC,CEAB于点E <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>AD于点F,若BC=2,EF的长为 .

1组合 3301

14题图

5.如图,小兰想测量南塔的高度她在 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 处仰望塔顶,测得仰角为30°,再往塔的方向前进50 m <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 处,测得仰角为60°,那么塔高约为 _________ m.(小兰身高忽略不计 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>


 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>







16.已知等腰三角形的腰长为2,腰上的高为1,则它的底角等于________

17.是我国古代著名的“赵爽弦图”的示意图,它是由四个全等的直角三角形围成的,若 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,将四个直角三角形中边长为6的直角边分别向外延长一倍,得到图所示的“数学风车”,则这个风车的外围周长是__________.

18. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ABC中,∠ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 90°AB=2BC,现给出下列结论:

sin A= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ;②cos B= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ;③tan A= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ;④tan B= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

其中正确的结论是 .(只需填上正确结论的序号)

三、解答题(共78

1 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 9.8分)计算下列各题:

(1) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> .

20.(8)如图,在Rt△ABC中,∠C=90°AB=10sin A= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,求BC的长和tan B的值.

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 0题图 21题图


21.10分)如图,在一笔直的海岸线l上有AB两个观测站,AB的正东方向,AB=2(单位:km.有一艘小船在点P处,从A测得小船在北偏西60°的方向,从B测得小船在北偏东45°的方向.

1)求点P到海岸线l的距离;

2)小船从点P处沿射线AP的方向航行一段时间后,到达点C处,此时,从B测得小船在北偏西15°的方向.求点C与点B之间的距离.(上述2小题的结果都保留根号)

2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>
 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>
2.10分)如图,为了测量某建筑物CD的高度,先在地面上用测角仪自A处测得建筑物顶部的仰角是30°,然后在水平地面上向建筑物前进了100 m,此时自B处测得建筑物顶部的仰角是45°.已知测角仪的高度是1.5 m,请你计算出该建筑物的高度.(取  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 1.732,结果精确到1 m


23.8分)如图,在梯形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

1)求 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 的值;(2)若 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 长度为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,求梯形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 的面积.


24.10分)如图,在一次数学课外实践活动中,小文在点C处测得树的顶端A的仰角为37°BC=20 m,求树的高度AB.

(参考数据: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

组合 3044







24题图



25.10分)如图,在小山的东侧 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 处有一热气球,以每分钟 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 的速度沿着仰角为60°的方向上升,20 min后升到 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 处,这时热气球上的人发现在 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 的正西方向俯角为45° <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 处有一着火点,求热气球的升空点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 与着火点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 的距离(结果保留根号).

26.14分)(2014·福州中考)如图(1),点O在线段AB上,AO2OB1OC为射线,且∠BOC60,动点P以每秒2个单位长度的速度从点O出发,沿射线OC做匀速运动,设运动时间为t.

1)当t <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 秒时,则OP SABP

2)当△ABP是直角三角形时,求t的值;

3)如图(2),当APAB时,过点AAQBP,并使得∠QOPB,求证:AQ·BP3.

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

26题图




24章 解直角三角形检测题参考答案

1.C 解析: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

2.D 解析: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 中,∵  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,∴  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,∴  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> .

3.C 解析: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> .

4.B 解析:如图,过点DDEABBC于点E,则四边形ABED是平行四边形,

BE=AD=6.

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

4题答图

ABAC,∴ DEAC.∵ CA是∠BCD的平分线,∴ CD=CE.

ADBC,∴ ∠ACB=∠DAC=∠DCA.∴ CD=AD=6.

BC=BE+CE=BE+CD=6+6=12.

AC= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> =8 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> .∴ tan B= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> =2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> .

5.C 解析:BN的长为x,则AN=9 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> x,由题意得DN=AN=9 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> x.因为DBC的中点,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> .Rt△BND中,∠B=90°,由勾股定理得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,即 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,解得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> .

6.C 解析: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,则 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 是直角三角形,且∠ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

所以在ABC中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

7 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> .A 解析: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> .由题意知 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,∴  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> .

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,又 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> .

根据条件还可以得出 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> .

A. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,故选项 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> A正确.

B. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,故选项B错误.

C. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,故选项C错误.

D.∵  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,∴  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>故选项D错误.

8.A 解析:先由坡比的定义,得BCAC=1∶ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> .BC=6 m,可得AC=6 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> m. Rt△ABC中,由勾股定理,得AB= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> =12(m).

9.B 解析:设小球距离地面的高度为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 小球水平移动的距离为  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 解得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

10.B 解析:设 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

又因为在菱形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 由勾股定理知 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

11.A 解析:设直角三角形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 直角边长分别为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

所以斜边长 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

12.B 解析:在锐角三角函数中仅当∠ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 45°时, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 选项错误;

因为45°A90°,所以B45°AB,所以BCAC,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,即 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 选项正确, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 选项错误;

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 1 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 1,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 选项错误.

13.> 解析:因为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,所以∠ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> .

14. <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 解析:过F点作FGBCAB于点G.

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 在△ABC中,AB=AC,ADBC边上的中线,

BD=CD= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> BC=1,BAD=CAD= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> BAC=15°,ADBC.

∵ ∠ACE= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> BAC,

∴ ∠CAD=ACE=15°,

AF=CF.

∵ ∠ACD=(180°30°)÷2=75°,

∴ ∠DCE=75°15°=60°.

RtCDF, CF= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> =2,DF=CD·tan 60°= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> .

14题答图

AF=CF,∴ AF=2.

FGBC,

GFBD=AFAD,GF1=2(2+ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ),

解得GF=42 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,

EFEC=GFBC,EF(EF+2)=(42 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> )2,

解得EF= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 1 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> .

15.43.3 解析:因为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> .

16.15°75° 解析:如图, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> .

在图中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,所以∠ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

在图中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,所以∠ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> .

组合 3345  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

1组合 3377 7.76 解析:如图,因为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,所以CD=12

由勾股定理得 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 所以这个风车的外围周长为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

18.②③④ 解析:因为∠C=90°AB=2BC,所以∠A=30°,∠B=60°,所以②③④正确.

19.解:(1 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> .

20.分析:由sin A= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 求出BC的长,根据勾股定理求出AC的长,利用tan B= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 求出tan B的值.

解:∵ sin A= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> AB=10,∴ BC=4.

AC= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> =2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,∴ tan B= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> .

21.分析:1)如图,过点PPDAB于点D,设PD= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> km,根据AD+BD=2列方程求解.

2)过点BBFCA于点F,在Rt△ABFRt△BFC中解直角三角形求解.

解:(1)如图,过点PPDAB于点D

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

21题答图


PD= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> km,由题意可知∠PBD=45°,∠PAD=30°

Rt△BDP中,BD=PD= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> km,Rt△PDA中,AD= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> PD= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> km.

AB=2 km,∴  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> =2.∴  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> = <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 1.

P到海岸线l的距离为( <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> km.

2)如图,过点BBFCA于点F.

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> Rt△ABF中,BF=AB·sin 30°=2× <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> =1km.

在△ABC中,∠C=180° <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> BAC <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ABC=45°.

Rt△BFC中,BC= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> BF= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ×1= <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> km.

C与点B之间的距离为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> km.

点拨:此题是解直角三角形在现实生活中的应用,通过构造直角三角形求解.当利用勾股定理或锐角三角函数不能直接求解时,常采用作垂线、引入未知数(一般为待定的数)构造方程求解.

22.解: <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,则由题意可知 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> m

Rt△AEC中,tan∠CAE <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,即tan 30° <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,即3x <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> (x100),解得x <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 5050 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> .

经检验 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 5050 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 是原方程的解.

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

故该建筑物的高度约为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

23.解:(1)  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> .

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> .

在梯形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 中,∵  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 3∠ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 30°  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 2)如图, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> .

Rt△ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,∴ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

Rt△ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 中, <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

梯形 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 的面积为 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

24.分析:利用解直角三角形求线段长,首先根据锐角三角函数的定义选取恰当的三角函数关系式,然后把已知的数据代入计算.本题根据锐角三角函数的定义得tan 37° <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,把 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>BC=20 m代入tan 37° <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 中求出树的高度AB.

:因为tan 37° <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>0.75BC=20 m,所以AB≈0.75×2015m.

25.解:过点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 于点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> . <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> .

因为∠ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 300 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> m

所以 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 300( <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 1) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 即热气球的升空点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 与着火点 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 的距离为300( <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 1) <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

26.1)解:1 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

2)解:①∵ ∠A<∠BOC60,∴ ∠A不可能是直角.

当∠ABP90时,如图所示(第26题答图(1)),

∵ ∠BOC60,∴ ∠OPB30.

OP <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 2OB,即2t2.∴ t1.

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

26题答图(1


当∠APB90时,如图所示(第26题答图(2)),作PDA <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> B,垂足为D,则∠ADPPDB90.

Rt△POD中,∵ ∠POD=60,∴ ∠OPD=30.

OP2t

ODtPD <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> tAD2tBD1t(△BOP是锐角三角形).

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

26题答图(2

方法一:BP2BD2+PD2=1t23t2AP2AD2+PD2=(2t)23t2.

BP2AP2AB2,∴ (1t)23t2(2t)23t29,即4t2t20.

解得t1 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> t2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> (舍去).

方法二:∵ ∠APDBPD90,∠BBPD90

∴ ∠APDB.∴ △APD∽△PBD.

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>PD2AD·BD.

于是( <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> t)2(2t)(1t),即4t2t20.

解得t1 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> t2 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> (舍去).

综上,当△ABP为直角三角形时,t1 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> .

3)证法一:∵ APAB,∴ ∠APBB.

如图所示(第26题答图(3)),作OE <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> AP,交BP于点E

∴ ∠OEBAPBB.

AQBP,∴ ∠QABB180.

又∵ ∠3OEB180,∴ ∠3QAB.

又∵ ∠AOC∠2B∠1QOP,∠BQOP

∴ ∠1∠2.

在△QAO和△OEP中,∵ ∠3QAO1∠2

∴ △QAO∽△OEP.

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,即AQ·EPEO·AO.

OEAP,∴ △OBE∽△ABP.

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> .∴ OE <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> AP1BP <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> EP.

AQ·BPAQ· <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> EP  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> AQ·EP <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> AO·EO <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 213.

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

26题答图(3

证法二:如图所示(第26题答图(4)),连接PQ,设APOQ相交于点F.

AQBP,∴ ∠QAPAPB.

APAB,∴ <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>APBB.∴ ∠QAPB.

又∵ ∠QOPB,∴ ∠QAPQOP.

在△QFA和△PFO中,∵ ∠QAFFOP,∠QFAPFO

∴ △QFA∽△PFO.∴  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,即 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> .

又∵ ∠PFQOFA,∴ △PFQ∽△OFA.∴ ∠3∠1.

∵ ∠AOC∠2B∠1QOP,∠BQOP

∴ ∠1∠2.∴ ∠2∠3.

∴ △APQ∽△BPO.∴  <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> .∴ AQ·BPAP·BO313.

 <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/180/" title="直角" class="c1" target="_blank">直角</a> <a href="/tags/387/" title="三角形" class="c1" target="_blank">三角形</a> <a href="/tags/848/" title="华东" class="c1" target="_blank">华东</a> <a href="/tags/913/" title="直角三角形" class="c1" target="_blank">直角三角形</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

26题答图(4




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