Thread: Straight 3-sided pyramid

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.

Where is alpha? Where is beta? Is alpha at vertex A and beta at vertex B? If so, you need to point that out. Is a the altitude of the the base triangle ABC? Is that line on the base even an altitude? What are all the A's around the pyramid. is a=5 as stated in the text or 6 as stated on the paper?

I've never heard of a straight pyramid. There are right pyramids.

The point where altitudes intersect is called the orthocenter.

Even if I make the given assumptions above that I stated, there is still not enough information to solve the problem. If the apex was directly above the orthocenter of the base, then this problem could be solved (not that it would be easy), but I (we) am not told this as a given.