题目内容
已知△
的内角
所对的边分别为
且
.
(1) 若
, 求
的值;
(2) 若△
的面积
求
的值.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823213642445475.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823213642476516.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823213642508452.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823213642601777.png)
(1) 若
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823213642788386.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823213643194433.png)
(2) 若△
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823213642445475.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823213643256619.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823213643272370.png)
(1)
.
(2)![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232136433191037.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232136433031228.png)
(2)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232136433191037.png)
本小题主要考查正弦定理、余弦定理、同角三角函数的基本关系等基础知识,考查运算求解能力。第一问中
,得到正弦值
,再结合正弦定理可知,
,得到
(2)中
即
所以c=5,再利用余弦定理
,得到b的值。
解: (1)∵
, 且
, ∴
. 由正弦定理得
, ∴
.
(2)∵
∴
. ∴c=5
由余弦定理得
,
∴![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232136437401852.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823213643334720.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823213643350908.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823213643366775.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232136433031228.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823213643256619.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232136434121052.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823213643444832.png)
解: (1)∵
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823213643334720.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823213643490522.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823213643350908.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823213643366775.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232136433031228.png)
(2)∵
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232136434121052.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823213643631723.png)
由余弦定理得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823213643444832.png)
∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232136437401852.png)
![](http://thumb.zyjl.cn/images/loading.gif)
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