Find 3rd point of triangle with the opposite angle

Question

I got a triangle, I know A and B coordinates, I know all angles, how can I calculate C coordinates?

Schema

Answer 1

I don't think you can. If you put A at $(-1,0)$ and B at $(0,1)$, then any point $C$ on the unit circle will make a right triangle with A and B. Which means the coordinates of A and B and the measure of the angle C are not enough. If you know one more side length or one more angle, you can use the law of sines to get the other measurements.