# A triangle has sides A, B, and C. Sides A and B have lengths of 2 and 6, respectively. The angle between A and C is (7pi)/24 and the angle between B and C is  (5pi)/24. What is the area of the triangle?

The opposite angle of side B(6) is$7 \cdot \frac{180}{24} = {52.5}^{0}$
The opposite angle of side A(6) is$5 \cdot \frac{180}{24} = {37.5}^{0}$
So it is a right angled triangle as the third angle is $180 - \left(52.5 + 37.5\right) = {90}^{0}$Hence the area of the triangle is $\frac{1}{2} \cdot 6 \cdot 2 = 6$ square units[Answer]