题目内容
(本小题满分14分)
在
中,角A、B、C的对边分别为a、b、c,且
,
,
边上的中线
的长为
.![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155423792332.jpg)
(Ⅰ) 求角
和角
的大小;
(Ⅱ) 求
的面积.
在
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155423231400.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155423433658.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155423683667.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155423699241.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155423714362.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155423761166.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155423792332.jpg)
(Ⅰ) 求角
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155423855200.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155423886206.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155423792332.jpg)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155423231400.gif)
(Ⅰ)![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155423948407.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155423995309.gif)
(Ⅱ)![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155424011707.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155423948407.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155423995309.gif)
(Ⅱ)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155424011707.gif)
解:(Ⅰ)由![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155424042989.gif)
∴
由
,得
即![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155424276519.gif)
则
,即
为钝角,故
为锐角,且![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155424338509.gif)
则
故
.
(Ⅱ)设
,由余弦定理得
,解得![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155424744232.gif)
故
.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155424042989.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155424135780.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155423948407.gif)
由
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155423683667.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155424260652.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155424276519.gif)
则
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155424291317.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155424307205.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155423886206.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155424338509.gif)
则
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231554243691395.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155423995309.gif)
(Ⅱ)设
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155424447275.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155424541884.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155424744232.gif)
故
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155424011707.gif)
![](http://thumb.zyjl.cn/images/loading.gif)
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