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angle between planes wanted, right triangular prism, S_ {ABE}+S_ {ACF}=S_{AEF}

Source: 2011 Romania District VIII P3

May 19, 2020
geometry3D geometryprismareasangles

Problem Statement

Let ABCA′B′C′ABCA'B'C' a right triangular prism with the bases equilateral triangles. A plane α\alpha containing point AA intersects the rays BB′BB' and CC′CC' at points E and FF, so that SABE+SACF=SAEFS_ {ABE} + S_{ACF} = S_{AEF}. Determine the measure of the angle formed by the plane (AEF)(AEF) with the plane (BCC′)(BCC').
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