Given that sinA = 3/5 and cosB = 12/13, where A is obtuse and B is acute, find the exact values of cos(A+B) and cot(A-B)

I know that cos(A+B) = cosAcosB - sinAsinB and that I need to draw a triangles of some sort with the sides 3 and 5 on one and 12 and 13 on the other, but I don't know how to find the last length because I don't think they would be right-angled triangles.

I know that cot = 1/tan

Where should I go from here?

Thanks,

Delta