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?
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?