# A triangle has sides A, B, and C. Sides A and B have lengths of 2 and 3, 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?

Area of $\Delta A B C = \cong 0.7764$ sq. unit.
Observe that the the third $\angle$, call it $\angle c$ btwn. sides B & A is, $\pi - 13 \frac{\pi}{24} - 3 \frac{\pi}{8} = \frac{24 \pi - 13 \pi - 9 \pi}{24} = 2 \frac{\pi}{24} = \frac{\pi}{12.}$
Now, use the well-known formula for area of $\Delta A B C$ :
Area of $\Delta A B C = \frac{1}{2} \cdot A \cdot B \cdot \sin \angle c = \frac{1}{2} \cdot 2 \cdot 3 \cdot \sin \left(\frac{\pi}{12}\right) = 3 \cdot \sin {15}^{0} = 3 \cdot 0.2588 \cong 0.7764$ sq. unit.