# A triangle has sides A, B, and C. Sides A and B have lengths of 8 and 11, respectively. The angle between A and C is (19pi)/24 and the angle between B and C is  (pi)/24. What is the area of the triangle?

Feb 20, 2016

22

#### Explanation:

The interior angles in a triangle add up to $\pi$. So the angle between $A$ and $B$ is given by

$\pi - \frac{\pi}{24} - \frac{19 \pi}{24} = \frac{\pi}{6}$

The area of the triangle is given by the formula

$\frac{1}{2} \times A \times B \times \sin \theta$

Therefore, the area of the above triangle is

$\frac{1}{2} \times 8 \times 11 \times \sin \left(\frac{\pi}{6}\right) = 22$