Check out the attached pic with the triangles and their data. I started out finding the missing sides using Pythagorem Theorem. Then I used the Law of Cosines to find angles A and B. I need to find the exact value of sin(A+B), but doing this doesn't result in answers that can use an addition or subtraction formula to get a "nice" exact value from the unit circle.....I've been kicked around by this problem for the last 2 days!!! Am I going about this wrong? If so, could someone shed some light on this for me?

Thanks,

~CC