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【332298】2.1 锐角三角比 分层练习

时间:2025-01-21 12:35:51 作者: 字数:1695字
简介:

2.1 锐角三角比

基础扫描

1. 在Rt△ABC中,∠C=90°abc分别是∠A、∠B、∠C的对边,若b=3a,则tanA=

2在△ABC中,∠C90°cosA <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>c4,则a_______

3. 如果 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 是等腰直角三角形的一个锐角,则 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 的值是(  )

A <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> B <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> C <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> D <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

4. 如图,P是∠α的边OA上一点,且P点坐标为(23),

sinα=_______cosα=_________tanα=______ _

5.如图,在△ABC中,∠ACB=90°CD⊥ABD,若 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,则tan∠ACD的值为( )

A <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> B <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> C <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> D <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

6.已知α是锐角,且cosα= <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,求sinαtanα的值.




能力拓展

7.若α为锐角,试证明: <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>




8组合 75 .如图,在Rt△ABC中,CDCE分别为斜边AB上的高和中线,BC=aAC=bba),若tan∠DCE= <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,求 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 的值.







创新学习

9.如图,Rt△ABC中,∠C=90°DCA上一点,∠DBC=30°DA=3AB= <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> ,试求cosAtanA的值.


 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>





参考答案

1 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 2 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 3B 4 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 5A

6. 解:如图,Rt△ABC中,∠C=90°,设∠A=α

 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

AC=3 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> AB=4 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>0),则BC= <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

7 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> . 证明:如图, <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> 中,∠C=90°,设∠A=α

 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  ∴ <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

又 ∵  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  ∴ <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> .

8 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> . 解:如图,∵ <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

DE= <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> DC=2 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>0)则  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> .

CERt△ABC斜边上的中线

BE=AE=CE= <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>  ∴ <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

9.解:在Rt△DBC中,∠C=90°,∠DBC=30°

 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

可设DC=kBC= <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> kk0).

Rt△ABC中,由勾股定理知: <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>

 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> .整理得 <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> .∴k=1

BC= <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a> CA=4.∴ <a href="/tags/48/" title="练习" class="c1" target="_blank">练习</a> <a href="/tags/179/" title="锐角" class="c1" target="_blank">锐角</a> <a href="/tags/920/" title="三角" class="c1" target="_blank">三角</a>