题目内容
(12分)在
ABC中,
, sinB=
.
(I)求sinA的值;
(II)设AC=
,求
ABC的面积.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215733021319.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215733037664.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215733068327.png)
(I)求sinA的值;
(II)设AC=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215733084341.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215733021319.png)
(Ⅰ)![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215733115679.png)
(Ⅱ)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215733115679.png)
(Ⅱ)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232157331462040.png)
(1) 由
ABC中,
,得![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215733474703.png)
。
∴![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215733115679.png)
(2)由(1)和正弦定理得
,
,![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232157335831260.png)
。
所以
。
解:(Ⅰ)由
,且
,∴
,∴
,
∴
,又
,∴![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215733115679.png)
(Ⅱ)如图,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232157338951188.png)
由正弦定理得![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215733552831.png)
∴
,又![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232157341601234.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232157336771052.png)
∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215733021319.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215733037664.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215733474703.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232157335051347.png)
∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215733115679.png)
(2)由(1)和正弦定理得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215733552831.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232157335671570.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232157335831260.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232157336771052.png)
所以
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232157337232056.png)
解:(Ⅰ)由
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215733739631.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215733770612.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215733474703.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232157338171487.png)
∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215733833964.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215733848513.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215733115679.png)
(Ⅱ)如图,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232157338951188.png)
由正弦定理得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823215733552831.png)
∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232157341451582.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232157341601234.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232157336771052.png)
∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232157342382069.png)
![](http://thumb.zyjl.cn/images/loading.gif)
练习册系列答案
相关题目