题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042210-18348.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042210-64824.png)
(Ⅰ)求角C的大小:
(Ⅱ)设角
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042210-68938.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042210-17300.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042210-50111.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042211-72911.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042211-33889.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042211-17871.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042211-57344.png)
解析
试题分析:(Ⅰ)(Ⅰ)∵
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042212-70714.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042212-26227.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042212-86554.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042212-74192.png)
得
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042213-36119.png)
∴C=
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042211-17871.png)
(Ⅱ)方法1:由已知
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042213-96179.png)
根据余弦定理可得:
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042213-47821.png)
(1)、(2)联立解得:
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042213-44444.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042213-17431.png)
方法2:
由正弦定理得:
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042214-18846.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042214-83386.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042214-32777.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042214-70727.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042215-87754.png)
方法3:由(Ⅰ)知C=
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042215-32827.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042213-96179.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042210-18348.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042215-22944.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042215-32576.png)
又. C=
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042215-32827.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042211-57344.png)
点评:解决该试题的关键是对于向量共线以及两角和差的三角关系式的变形求解,同时能结合三角形的两个定理来确定形状,属于基础题。
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042205-91781.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042205-51559.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042205-67759.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042205-28131.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042206-28915.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042206-30635.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042206-14644.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042206-16248.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042206-53781.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042207-81104.png)
A.8 | B.16 | C.32. | D.64 |
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042155-11928.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042156-98227.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042156-82944.png)
(Ⅰ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042156-60093.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042156-93772.png)
(Ⅱ)在
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042156-82127.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042157-13689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042157-67757.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042157-21911.png)
若a、b、c是△ABC三个内角A、B、C所对边,且
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042148-88690.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042148-87167.png)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042149-44857.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042149-56168.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042146-12450.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042140-64855.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042140-71318.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020042141-13399.png)
A.18 | B.3 | C.15 | D.9 |
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