Base of the pyramid is a triangle with a = 5 and angles alpha = 47°, beta = 53°. The angle between side edge and the base phi (φ) = 50°. What's the pyramid's height (and volume)? Being a straight pyramid, it does mean that side edges are equal in length, right?
http://shrani.si/f/X/Vk/1OqVN4mv/scan0001.jpg
What am I missing here? Does the pyramid height cross the "altitude point" of the triangle (the point where the triangle's altitudes intersect; is "altitude point" the right word?)? Is there anything about the crossing of "branch"/"leg" of the phi angle and the a side of the triangle?
