The Trigonometry Height Shortcut
While trying to derive a generic solution for this problem, my prized math student and I found this solution. The derivation included using the cosine and sin addition identities.
the code for TI 85-86
02:Outpt(1,1,"This is for height")
03:Outpt(2,4,"Angles in degrees")
10:D*sin alpha * sin beta/sin( abs( alpha - beta )) -> H
12:Outpt(1,1,"The height is: ")
BTW, this was my first program written in this type of langage (Basic I think), so please feel free to make any modifications. The reason for the abs is so that alpha is not required to be larger than beta.