Well, you know the top tube length, and seat tube length, and the interior angle where these two tubes meet, and let's call that A. And let's call the end point of the top tube B, and end point of the seat tube C. It's simple trig to find the dimensions of the triangle. The head tube length actually doesn't matter here. From there, it's just a matter of finding the height of the triangle from point C to line AB, and, and the length from where the height line bisects line-AB to point B for reach.

This should be pretty simply, am I missing something here?