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angle between lateral edge of pyramid and plane of base wanted

Source: 2011 Romanian NMO grade VIII P3

May 18, 2020
pyramidangle3D geometrygeometry

Problem Statement

Let VABCVABC be a regular triangular pyramid with base ABCABC, of center OO. Points II and HH are the center of the inscribed circle, respectively the orthocenter △VBC\vartriangle VBC. Knowing that AH=3OIAH = 3 OI, determine the measure of the angle between the lateral edge of the pyramid and the plane of the base.
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