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?