MathDB
MMO 012 Moscow MO 1935 unfolding lateral surface of cone, angle wanted

Source:

July 17, 2019
geometry3D geometryconepyramidangles

Problem Statement

The unfolding of the lateral surface of a cone is a sector of angle 120o120^o. The angles at the base of a pyramid constitute an arithmetic progression with a difference of 15o15^o. The pyramid is inscribed in the cone. Consider a lateral face of the pyramid with the smallest area. Find the angle α\alpha between the plane of this face and the base.