2016 AIME I Problems/Problem 4
A right prism with height has bases that are regular hexagons with sides of length . A vertex of the prism and its three adjacent vertices are the vertices of a triangular pyramid. The dihedral angle (the angle between the two planes) formed by the face of the pyramid that lies in a base of the prism and the face of the pyramid that does not contain measures degrees. Find .
Let and be the vertices adjacent to on the same base as , and let be the last vertex of the triangular pyramid. Then . Let be the foot of the altitude from to . Then since is a triangle, . Since the dihedral angle between and is , is a triangle and . Thus .
(Solution by gundraja)
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