题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032840-36061.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032840-48273.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032841-77268.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032841-50343.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032841-43030.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032841-26509.png)
(Ⅰ)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032841-45968.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032841-50343.png)
(Ⅱ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032841-31451.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032841-46057.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032841-27979.png)
解析
(1)要证明线面垂直关键是证明线线垂直,BA垂直于平面ASD。
(2)利用等价转化思想,通过求解点到面的距离得到线面角的求解。
解:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032842-97906.jpg)
(I)取AB中点E,连结DE,则四边形BCDE为矩形,DE=CB=2,
连结SE,则
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032842-45260.png)
又SD=1,故
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032842-93544.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032842-54046.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032842-28147.png)
得
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032842-25599.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032842-87229.png)
SD与两条相交直线AB、SE都垂直。
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032842-31273.png)
(II)由
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032842-25599.png)
平面
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032842-45162.png)
作
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032842-46965.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032843-98429.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032843-10932.png)
作
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032843-29070.png)
连结SG,则
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032843-98311.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032843-33778.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032843-62605.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032843-98429.png)
作
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032844-35982.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032844-66289.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032844-18123.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032844-98435.png)
由于ED//BC,所以ED//平面SBC,E到平面SBC的距离
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032845-56659.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032844-98435.png)
设AB与平面SBC所成的角为
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032845-44185.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032845-46708.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032819-20828.png)
⑴求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032819-76921.png)
⑵求异面直线
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032820-19274.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032820-26375.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032820-96045.jpg)
A.直角三角形 | B.锐角三角形 | C.钝角三角形 | D.以上都有可能 |
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032812-69876.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032812-93985.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032800-53245.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032801-51240.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032801-69539.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032801-94274.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032801-94776.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032801-59674.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032801-23125.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032801-71710.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032801-94776.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032801-65429.png)
A.2 B.
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032756-61518.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191106/20191106032757-92954.png)
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