I'm struggling to find an answer to this problem, I would be grateful to anyone that can help.

Essentially I need to find the XY co-ordinates of point (corner) B on the scalene triangle in figure 1 (sorry about the quick, crude drawing). Point A is always in a static location and point C is not static, but can always be found relative to the location of A.

The information I know is the XY co-ordinates of points A and C. From this I can find the length of side AC. Conveniently, I also know that sides BC and AB are a constant length, defined beforehand, which should also help. I think the only angle I can find is that between points A and C.

Imagine the problem like this. I hold out my arm, with my shoulder and elbow bent at arbitrary angles. I know the length from my shoulder to my elbow (side AB) and I know the length from my elbow to my fingertip (side BC) (I have measured them beforehand). I know where my shoulder (point A) is and I know where my fingertip (point C) is in relation to it.

- I want to find out where my elbow (point B) is from this information.

I can find this using several stages, I'm closing in on an algorithm to solve it that breaks down this triangle into right angle triangles. However, I'm convined that this problem must in fact have a fairly simple solution that I can't see.

Figure 1.