题目内容
(本小题满分13分)
已知三点A(3,0),B(0,3),C
,
.
(1)若
,求角
;
(2)若
,求
的值.
已知三点A(3,0),B(0,3),C
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190731836499.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190731851509.gif)
(1)若
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190731867464.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190731883192.gif)
(2)若
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190731914454.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190731929658.gif)
解:(1) ∵![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190731945935.gif)
···························· 2分
由![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/2014082319073197665.gif)
得
········································ 4分
整理得![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190732023461.gif)
∴
····························································································· 6分
∵
∴
·································································· 7分
(2) ∵![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190731914454.gif)
∴
····························································· 8分
即
····················································································· 9分
∴
∴
················································································· 10分
∴
································· 13分
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190731945935.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/2014082319073196165.gif)
由
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/2014082319073197665.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190731992440.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190732007826.gif)
整理得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190732023461.gif)
∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190732054398.gif)
∵
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190731851509.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190732085407.gif)
(2) ∵
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190731914454.gif)
∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190732117778.gif)
即
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190732132559.gif)
∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190732148617.gif)
∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823190732163574.gif)
∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231907321791773.gif)
略
![](http://thumb.zyjl.cn/images/loading.gif)
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