I made a diagram in GeoGebra in order to model this problem. I'm not sure it's possible in that program to include all the constraints I want (for example, I can't seem to lock the 90° angle of the shock absorber), so I had to go by successive approximation, and this is what I came up with, at three decimal places precision:

That gives the angle as 101.115°, which is certainly precise enough for LDraw. Still just a tad unsatisfying, because I don't have a method, just a result…but it is at least a result.

That gives the angle as 101.115°, which is certainly precise enough for LDraw. Still just a tad unsatisfying, because I don't have a method, just a result…but it is at least a result.