# A triangle has sides A, B, and C. Sides A and B have lengths of 2 and 1, respectively. The angle between A and C is (13pi)/24 and the angle between B and C is  (3pi)/8. What is the area of the triangle?

$\sin \left(\frac{\pi}{12}\right)$
The third angle is $\pi - \left(13 \frac{\pi}{24} + 3 \frac{\pi}{8}\right) = \frac{\pi}{12}$.
The altitude to the side A is 1 X $\sin \left(\frac{\pi}{12}\right) = \sin \left(\frac{\pi}{12}\right)$.
Area = (base X altitude)/2 = (2 X sin(pi/12))/2 = sin(pi/12).