Dihedral Angle in a Triangular Pyramid
Source: 2016 AIME I #4
March 4, 2016
2016 AIME IAIME3D geometrygeometryprismpyramid
Problem Statement
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 . Find .