How to find the height of an oblique cone?

Question

Mathematics

How to find the height of an oblique cone if the length of the generatrix is ​​known, and 2 orthogonal angles at its vertex alpha and beta. (An analogy of how to find the height of an aircraft above the ground knowing the height of the radio altimeter, tonnage and roll).
There are thoughts like this:

H = L * cos ( sqrt (( a * a ) + ( b * b )) * DEGTORAD  + (( a + b ) / 6)  *  DEGTORAD );

But there is some inaccuracy here.

Answer 1

It is not clear what the corners are between what and what.
Specifications: "length", "beta", "radio altimeter", "pitch".