Since you are going to know the angle (you set the servo position) and the extension, you can draw an imaginary line to the base (or the top) as one side of a right triangle.. Which is your opposing side to the known angle.
I have been working through this myself for a suspension plotter project.. You are basically doing the same thing, calculating the height of an imaginary triangle given a couple of known distances and angles. The key to all of it is making it into a calculatable triangle to determine position.
Pythagorean can take it from there..