AutoCad :: Angle To Put A Line Of Specific Length Between Parallel Lines

I am drawing a diagram to describe a mathematical word problem. Since it is easier to visualize with a drawing, I want to draw it using the given dimensions. But angles used in the diagram are unknown and are not needed for the answer to be calculated, so the only way to draw this freehand is to guess at the angle resulting in the correct distances to be off.

Here is the word problem: There are two ladders, one 40 feet and the other 30 feet, each touching the base of one of two buildings and leaning against the other building. If the ladders cross 10 feet above the ground, how far apart are the buildings?

So for my drawing, being rather simple considering what AutoCAD can do, results in this:

Can AutoCAD calculate the angle needed to place a line of a given length between two parallel lines that are a distance apart less than the length of the line to place between them, having the endpoints of this line touching the parallel lines, fitting exactly?

For the word problem, the distance between the two parallel lines is what needs to be solved and the math is quite invloved, having to find the roots or solution of a quartic equation. (I have the solution figured out to be 26.03287754 feet)

What I am afraid of is that this would require to program an AutoLISP routine to create a new command that one can call from the command line. I see it using the the measure command with relative and absolute co-ordinates. This may be far from a "beginner" question. I can do this quite easily on a peice of paper: having two parallel lines drawn, take a ruler and placing the "0" mark on one line, then adjusting the angle until the desired length just reaches the opposite parallel line. I used to use this trick quite often when drafting with pencil and paper to divide a distance into a required number of even amounts, so this can't be that difficult to do with AutoCAD!