# A triangle has sides A, B, and C. Sides A and B have lengths of 10 and 8, respectively. The angle between A and C is (11pi)/24 and the angle between B and C is  (7pi)/24. What is the area of the triangle?

The area of triangle is $28.28$ Sq.unit
The Angle between sides A & B is $\angle C = \pi - \left(11 \cdot \frac{\pi}{24} + 7 \cdot \frac{\pi}{24}\right) = \frac{\pi}{4} = {45}^{0}$
We know the area of triangle with two sides A & B and their included angle is $\frac{s i \mathrm{de} A \cdot s i \mathrm{de} B \cdot \sin C}{2} = 10 \cdot 8 \cdot \sin \frac{45}{2} = 28.28$ square unit[Ans]