题目内容
已知
中,
的对边分别为
,且
, ![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221424153352.png)
(1)若
,求边
的大小;
(2)求
边上高的最大值.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221424075544.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221424090516.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221424106450.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221424121933.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221424153352.png)
(1)若
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221424168617.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221424184249.png)
(2)求
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221424199402.png)
(1)
(2)
的最大值为
.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221424231536.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221424246313.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221424262449.png)
(1)由
通过降幂公式化简整理可得B的值.又已知A角,所以由正弦定理可求出c的值.
(2)设
边上的高为
,根据面积公式![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232214243401200.png)
可得
,由余弦定理![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232214243871090.png)
可得
,所以高的最大值确定
(1)
,
,![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221424465851.png)
所以
或
(舍),得
3分
,则
,
,得
6分
(2)设
边上的高为
,
,
,
又
,
10分
,当
时取到等于号所以
边上的高
的最大值为
.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221424121933.png)
(2)设
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221424199402.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221424246313.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232214243401200.png)
可得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221424355702.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232214243871090.png)
可得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221424402400.png)
(1)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221424418752.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221424449885.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221424465851.png)
所以
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221424480616.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221424511482.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221424527540.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221424168617.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221424574527.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221424589729.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221424231536.png)
(2)设
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221424199402.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221424246313.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221424683927.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232214243401200.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221424714727.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232214247451080.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221424761425.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221424792823.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221424808354.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221424199402.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221424246313.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823221424262449.png)
![](http://thumb.zyjl.cn/images/loading.gif)
练习册系列答案
相关题目