# A triangle has sides A, B, and C. Sides A and B have lengths of 7 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?

Mar 28, 2016

Area of triangle is $19.799$

#### Explanation:

As angle between A and C is $11 \frac{\pi}{24}$ and the angle between B and C is $7 \frac{\pi}{24}$, angle between A and B is

$\pi - \frac{11 \pi}{24} - \frac{7 \pi}{24} = \frac{6 \pi}{24} = \frac{\pi}{4}$

Area of triangle is given by $\frac{1}{2} a b \sin C$ and hence it is

$\frac{1}{2} \times 7 \times 8 \times \sin \left(\frac{\pi}{4}\right) = \frac{28}{\sqrt{2}} = 19.799$