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Another solid geometry

Source: Romanian District Olympiad 2006, Grade 8, Problem 1

March 11, 2006
geometrytrigonometryvector

Problem Statement

On the plane of triangle ABCABC with ∠BAC=90∘\angle BAC = 90^\circ we raise perpendicular lines in AA and BB, on the same side of the plane. On these two perpendicular lines we consider the points MM and NN respectively such that BN<AMBN < AM. Knowing that AC=2aAC = 2a, AB=a3AB = a\sqrt 3, AM=aAM=a and that the plane MNCMNC makes an angle of 30∘30^\circ with the plane ABCABC find a) the area of the triangle MNCMNC; b) the distance from BB to the plane MNCMNC.
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