# A triangle has sides A, B, and C. Sides A and B have lengths of 1 and 5, respectively. The angle between A and C is (7pi)/24 and the angle between B and C is  (pi)/8. What is the area of the triangle?

$5 \frac{\sqrt{3} + 1}{4 \sqrt{2}}$ areal units = 0.9859 areal units, nearly..
Using the sum of the angles is $\pi$, the third angle between side A and B is $7 \frac{\pi}{12}$.
The area is $\frac{1}{2} A B \sin \left(\angle b e t w e e n A \mathmr{and} B\right)$
$\sin \left(7 \frac{\pi}{12}\right) = \sin \left(\frac{\pi}{3} + \frac{\pi}{4}\right)$