# A triangle has sides A, B, and C. Sides A and B have lengths of 2 and 4, respectively. The angle between A and C is (13pi)/24 and the angle between B and C is  (5pi)/24. What is the area of the triangle?

$2 \sqrt{2}$
Sides a, b are given and the angle between these two would be $2 \pi - \left(\frac{13 \pi}{24} + \frac{5 \pi}{24}\right)$ = $\frac{5 \pi}{4}$
Area would be $\frac{1}{2} a b \sin \left(\frac{5 \pi}{4}\right)$= $\frac{1}{2} \left(2\right) \left(4\right) \frac{\sqrt{2}}{2}$= $2 \sqrt{2}$