题目内容
在
中,
为锐角,角
所对的边分别为
,且![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232212502411000.png)
(I)求
的值;
(II)若
,求
的值.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221250131544.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221250147415.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221250194512.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221250209446.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232212502411000.png)
(I)求
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221250256423.png)
(II)若
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221250272569.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221250209446.png)
(I)
(II)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221250319635.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221250350352.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221250365612.png)
(I)可以通过求A+B的某一个三角函数值来求角,本小题可以通过求A+B的余弦值,要注意对A+B的范围进行分析,从而确定出A+B的大小.
(II)在(I)的基础上,可确定
,进而可由正弦定理
得
,再结合
,可求出a,b,c的值
(I)∵
为锐角,
∴![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232212505061936.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232212505372569.png)
∵
∴
(II)由(I)知
,∴ ![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221250615689.png)
由
得
,即![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221250428701.png)
又∵
∴
∴
∴ ![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221250365612.png)
(II)在(I)的基础上,可确定
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221250381592.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221250412984.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221250428701.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221250272569.png)
(I)∵
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221250147415.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232212502411000.png)
∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232212505061936.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232212505372569.png)
∵
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221250553627.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221250319635.png)
(II)由(I)知
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221250381592.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221250615689.png)
由
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221250412984.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221250677783.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221250428701.png)
又∵
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221250272569.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221250740611.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221250350352.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221250365612.png)
![](http://thumb.zyjl.cn/images/loading.gif)
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