题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044627-37244.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044628-86729.png)
(1)求角C;
(2)求边a。
答案
解析
①由已知条件,在直角三角形中,利用角C的正弦可求角C;
②在△ABC中,利用余弦定理,结合①得结论可求
解:△ABC为锐角三角形,过A作AD⊥BC于D点,D在线段BC上,
sinC=
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044628-52880.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044628-85134.png)
又由余弦定理知:(
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044627-37244.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044628-71541.png)
即a2-4a-5=0 ∴a=5或a=-1(舍去)
因此所求角C=60°,a=5
核心考点
举一反三
设
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044621-50132.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044621-91846.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044622-30528.png)
(Ⅰ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044621-50132.png)
(Ⅱ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044622-52967.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044615-93619.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044615-71174.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044615-30704.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044615-83893.png)
(Ⅰ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044616-55780.png)
(Ⅱ)现给出三个条件:①
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044616-22576.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044616-69171.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044616-42504.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044615-93619.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044615-93619.png)
已知
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044606-51958.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044606-74359.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044607-31167.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044607-47974.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044607-89167.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044607-92287.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044608-90961.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044608-47462.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044608-17856.png)
(1)求角
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044607-47974.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044608-52221.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044608-55643.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044607-89167.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044607-92287.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044558-45313.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044558-66133.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044558-95796.png)
且
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044558-19934.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044559-36859.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044559-75595.png)
求(1)角
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044559-86174.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044559-58380.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044552-69628.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044553-49290.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044553-68822.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020044553-68822.png)
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