名校
解题方法
1 . 如图,三棱锥P-ABC所有棱长都等,PO⊥平面ABC,垂足为O.点
,
分别在平面PAC,平面PAB内,线段
,
都经过线段PO的中点D.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/26/13c2d66b-2663-4b89-9803-feac31cc495c.png?resizew=212)
(1)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15e54038fa9518fc9a3aa2cb97a74196.png)
平面ABC;
(2)求直线AP与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0758f3ff9f1f7109024c1ef65536c58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/211b9e53e4677ae9e2b20d5f7ce0a4e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86814dbae9a5343d69bb4647900b3bfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbb16f7dbc4b9993c4efa0764df1d8ca.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/26/13c2d66b-2663-4b89-9803-feac31cc495c.png?resizew=212)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15e54038fa9518fc9a3aa2cb97a74196.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7003aee0b4b85f0fdd48ca9ae5826d54.png)
(2)求直线AP与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d41f793cfb36b09c1f67f75ccf9cef1.png)
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