# A triangle has sides A, B, and C. Sides A and B are of lengths 6 and 5, respectively, and the angle between A and B is (7pi)/12 . What is the length of side C?

C = sqrt( 61 + 15sqrt2(sqrt3-1)
C^2 = A^2 + B^2 - 2A B cos (7pi/12) = 61-60 cos(7pi/12)$\cos \left(7 \frac{\pi}{12}\right) = \cos \left(4 \frac{\pi}{12} + 3 \frac{\pi}{12}\right) = \cos \left(\frac{\pi}{4} + \frac{\pi}{3}\right)$