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第二十六章　解直角三角形
26.3 解直角三角形
INCLUDEPICTURE"复习回顾.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\复习回顾.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\复习回顾.tif" \* MERGEFORMATINET
1．如图，某游乐园彩虹滑梯的高度为h，滑梯的坡角为α，那么该彩虹滑梯的长度l为(　　)
INCLUDEPICTURE"image3357.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\image3357.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\image3357.tif" \* MERGEFORMATINET
(第1题)　
A. B．h·sin α C. D.
2．[2023烟台期中]如图，已知△ABC的三个顶点均在正方形网格的格点上，则下列结论错误的是(　　)
INCLUDEPICTURE"image3363.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\image3363.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\image3363.tif" \* MERGEFORMATINET
(第2题)　
A．cos C＝ B．tan B·tan C＝1 C．sin B＝sin C D．tan B＝
3．在△ABC中，∠C＝90°，cos A＝，BC＝10，则AB＝________．
4．如图，在Rt△ABC中，∠C＝90°，BC＝12，tan A＝，求AB的值．
INCLUDEPICTURE"image3376.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\image3376.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\image3376.tif" \* MERGEFORMATINET
INCLUDEPICTURE"预习效果检测.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\预习效果检测.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\预习效果检测.tif" \* MERGEFORMATINET
1．在直角三角形中，除直角外，还有________和__________共五个元素．由这五个元素中的已知元素求出其余未知元素的过程，叫做解直角三角形．
2．如图，在Rt△ABC中，已知∠C＝90°，a＝4，c＝8，解这个直角三角形．
INCLUDEPICTURE"image3379.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\image3379.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\image3379.tif" \* MERGEFORMATINET
INCLUDEPICTURE"课堂导学.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\课堂导学.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\课堂导学.tif" \* MERGEFORMATINET
INCLUDEPICTURE"W21.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\W21.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\W21.tif" \* MERGEFORMATINET 知识点1 解直角三角形
INCLUDEPICTURE"L1.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\L1.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\L1.tif" \* MERGEFORMATINET [2023广州越秀区二模在△ABC中，∠C＝90°，AB＝15，sin B＝，则BC等于(　　)
A．25 B．12 C．9 D．16
变式1如图，在△ABC中，AB＝AC＝13，BD⊥AC于点D，sin A＝.
INCLUDEPICTURE"image3382.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\image3382.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\image3382.tif" \* MERGEFORMATINET
(1)求BD的长；
(2)求tan C的值．
　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　
知识点2 解非直角三角形
INCLUDEPICTURE"L2.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\L2.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\L2.tif" \* MERGEFORMATINET 如图，在△ABC中，∠B＝30°，∠C＝45°，AC＝2，求AB和BC的长．
INCLUDEPICTURE"image3383.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\image3383.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\image3383.tif" \* MERGEFORMATINET
变式2[2023北京海淀区期末]已知在△ABC中，∠A＝60°，AB＝1＋，AC＝2，则∠C＝(　　)
A．45° B．75° C．90° D．105°
第二十六章　解直角三角形
26.3 解直角三角形
INCLUDEPICTURE"复习回顾.tif" INCLUDEPICTURE "复习回顾.tif" \* MERGEFORMAT INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\复习回顾.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\复习回顾.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\复习回顾.tif" \* MERGEFORMATINET
1．D　2.C　3.10
4．解：∵∠C＝90°，BC＝12，tan A＝＝，∴AC＝16.
∵AB2＝AC2＋BC2，∴AB＝＝20.
INCLUDEPICTURE"预习效果.tif" INCLUDEPICTURE "预习效果.tif" \* MERGEFORMAT INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\预习效果.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\预习效果.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\预习效果.tif" \* MERGEFORMATINET
1．三条边；两个锐角
2．解：在Rt△ABC中，∵a2＋b2＝c2，a＝4，c＝8，
∴b＝＝＝4 .
∵sin A＝＝＝，
∴∠A＝30°，∴∠B＝90°－30°＝60°.
INCLUDEPICTURE"课堂导学.tif" INCLUDEPICTURE "课堂导学.tif" \* MERGEFORMAT INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\课堂导学.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\课堂导学.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\课堂导学.tif" \* MERGEFORMATINET
例1　B
变式1.解：(1)∵AB＝13，BD⊥AC于点D，sin A＝，
∴＝， 即＝，解得BD＝12.
(2)∵AB＝13，BD＝12，BD⊥AC，∴AD＝5.
∵AC＝13，∴DC＝8，
∴tan C＝＝＝.
例2　解：过点A作AD⊥BC于点D.
∵在Rt△ACD中，∠ACD＝45°，AC＝2，
∴AD＝CD＝.
∵在Rt△ABD中，∠B＝30°，AD＝，
∴BD＝＝，AB＝＝2 .
∴BC＝CD＋BD＝＋.
变式2.B

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