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?

Exoneration: I'm reposting my thread, as it seems less precarious than bumping the old one. I also can't come up with any new idea.