题目内容
(本题10分).在
中,
,
,
.
(1)求
的值;(2)求
的值.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823232523038544.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823232523225542.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823232523428443.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823232523444631.png)
(1)求
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823232523475430.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823232523491556.png)
(1)
.(2)
.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823232523506727.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823232523537802.png)
(1)由
,可得
,再利用正弦定理
可求得
.
(2)先由余弦定理:
得:
,
进而得到b=2.再利用数理积的定义得
代入求值即可.
(1)在
中,由
,得
, 又由正弦定理:
得:
. ……………4分
(2)由余弦定理:
得:
,
即
,解得
或
(舍去),所以
. ……8分
所以,![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823232523491556.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232325240991367.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823232524115791.png)
即
.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823232523444631.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823232523600668.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823232523631836.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823232523506727.png)
(2)先由余弦定理:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232325236781010.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823232523693771.png)
进而得到b=2.再利用数理积的定义得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232325237091130.png)
(1)在
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823232523038544.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823232523444631.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823232523600668.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823232523631836.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823232523506727.png)
(2)由余弦定理:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232325236781010.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823232523693771.png)
即
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823232523959698.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823232523990403.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823232524037483.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823232524052494.png)
所以,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823232523491556.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232325240991367.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823232524115791.png)
即
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823232523537802.png)
![](http://thumb.zyjl.cn/images/loading.gif)
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