题目
题型:不详难度:来源:
如图5所示,四棱锥P-ABCD的底面ABCD是半径为R的圆的内接四边形,其中BD是圆的直径,∠ABD="60°," ∠BDC=45°,PD垂直底面ABCD,PD=
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020033-54550.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020034-41104.gif)
(1)求BD与平面ABP所成角θ的正弦值;
(2)证明:△EFG是直角三角形;
(3)当
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020034-21923.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020034-93237.jpg)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020034-79183.gif)
(2)证明见解析。
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020034-14535.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020035-99414.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020035-48972.gif)
(1)在
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020035-23000.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020035-40060.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020035-12202.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020036-49403.gif)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020036-81081.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020036-15210.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020036-81081.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020036-76520.gif)
设点
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020036-88032.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020037-62535.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020037-35880.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020037-82546.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020037-98089.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020037-78441.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020038-78794.gif)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020038-15030.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020038-11205.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020038-91051.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020039-70739.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020039-21389.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020039-22669.gif)
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020039-71944.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020039-14389.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020040-24478.gif)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020040-26495.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020039-22669.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020040-45494.gif)
核心考点
试题【(本小题满分14分)如图5所示,四棱锥P-ABCD的底面ABCD是半径为R的圆的内接四边形,其中BD是圆的直径,∠ABD="60°," ∠BDC=45°,PD垂】;主要考察你对线线角等知识点的理解。[详细]
举一反三
如图,已知点P在正方体ABCD-
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020019-78228.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020019-18845.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020020-45143.gif)
(Ⅰ)求DP与
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020020-55557.gif)
(Ⅱ)求DP与平面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020020-13852.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020020-73370.jpg)
三棱锥被平行于底面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020002-44431.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020002-40991.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020002-50584.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020002-11398.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020002-44431.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020002-10438.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020002-96549.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020002-69987.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020003-36310.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020003-87360.gif)
(Ⅰ)证明:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020003-37825.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020003-76232.gif)
(Ⅱ)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020003-91115.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022020003-65625.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022015955-61586.jpg)
在正方体
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022015955-94272.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022015955-26893.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022015956-76302.gif)
如图,四棱锥P—ABCD中,底面ABCD为矩形,PD垂直于底面ABCD,AD=PD=2,
E、F分别为CD、PB的中点.
(1)求证:EF⊥平面PAB;
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022015948-15857.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022015948-84201.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022015948-21144.jpg)
(1)求异面直线
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022015937-12827.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022015937-38136.gif)
(2)求点A到EF的距离.
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022015937-44558.gif)
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