# A triangle has sides A, B, and C. The angle between sides A and B is (5pi)/12 and the angle between sides B and C is pi/6. If side B has a length of 2, what is the area of the triangle?

In this triangle the angle between $A$ and $C$ is $\pi - \frac{\pi}{6} - \frac{5 \pi}{12} = \frac{5 \pi}{12}$ so we have an iscoseles triangle, thus $C = 2$.
The area is $P = \frac{1}{2} B C \sin \left(\angle \left(B , C\right)\right) = \frac{1}{2} \cdot 2 \cdot 2 \cdot \sin \left(\frac{\pi}{6}\right) = 1$.