# A triangle has sides A, B, and C. Sides A and B have lengths of 7 and 4, respectively. The angle between A and C is (3pi)/8 and the angle between B and C is  (pi)/12. What is the area of the triangle?

$\angle C = \pi - \left(\frac{3 \pi}{8} + \frac{\pi}{12}\right) = \frac{13 \pi}{12} , A r e a = \frac{1}{2} a b \sin C = \frac{1}{2} \left(7\right) \left(4\right) \sin \left(\frac{13 \pi}{24}\right) \approx 13.88 u n i {t}^{2}$
Start by adding the two given angles then subtract it from $\pi$ to get the measure of angle C. Then substitute in the lengths for sides a and b and the measure of angle C to the area formula and calculate.