如图①,△BCD内接于直角梯形A1A2A3D,A1D∥A2A3,A1A2⊥A2A3,A1D=10,A1A2=8,沿△BC
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如图①,△BCD内接于直角梯形A1A2A3D,A1D∥A2A3,A1A2⊥A2A3,A1D=10,A1A2=8,沿△BCD三边将△A1BD、△A2BC、△A3CD翻折上去,恰好形成一个三棱锥ABCD,如图②.
![](http://img.wesiedu.com/upload/2/2d/22d304446325a11de4b5bdbe545a94ec.jpg)
(1)求证:AB⊥CD;
(2)求直线BD和平面ACD所成的角的正切值;
(3)求四面体ABCD的体积.
![](http://img.wesiedu.com/upload/2/2d/22d304446325a11de4b5bdbe545a94ec.jpg)
(1)求证:AB⊥CD;
(2)求直线BD和平面ACD所成的角的正切值;
(3)求四面体ABCD的体积.
![如图①,△BCD内接于直角梯形A1A2A3D,A1D∥A2A3,A1A2⊥A2A3,A1D=10,A1A2=8,沿△BC](/uploads/image/z/18517837-13-7.jpg?t=%E5%A6%82%E5%9B%BE%E2%91%A0%EF%BC%8C%E2%96%B3BCD%E5%86%85%E6%8E%A5%E4%BA%8E%E7%9B%B4%E8%A7%92%E6%A2%AF%E5%BD%A2A1A2A3D%EF%BC%8CA1D%E2%88%A5A2A3%EF%BC%8CA1A2%E2%8A%A5A2A3%EF%BC%8CA1D%3D10%EF%BC%8CA1A2%3D8%EF%BC%8C%E6%B2%BF%E2%96%B3BC)
(1)证明:∵在直角梯形A1A2A3D中,A1B⊥A1D,A2B⊥A2C,∴在三棱锥ABCD中,AB⊥AD,AB⊥AC.∵AC∩AD=A,∴AB⊥平面ACD.∵CD⊂平面ACD,∴AB⊥CD.(2)由(1)知AB⊥平面ACD,∴AD为BD在平面ACD内的射影,∠BDA...
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