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another problem about parallelepipeds

Source: Romanian District Olympiad 2016, Grade VIII, Problem 4

October 4, 2018
geometry3D geometry

Problem Statement

Let ABCDA’B’C’D’ ABCDA’B’C’D’ a right parallelepiped and M,N M,N the feet of the perpendiculars of BD BD through A’, A’, respectively, C’. C’. We know that AB=2,BC=3,AA’=2. AB=\sqrt 2, BC=\sqrt 3, AA’=\sqrt 2.
a) Prove that A’M⊥C’N. A’M\perp C’N. b) Calculate the dihedral angle between the plane formed by A’MC A’MC and the plane formed by ANC’. ANC’.
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