# A triangle has sides A, B, and C. Sides A and B have lengths of 8 and 3, respectively. The angle between A and C is (13pi)/24 and the angle between B and C is  (pi)24. What is the area of the triangle?

Feb 3, 2018

$11.591$

#### Explanation:

Since angle B is $\frac{13 \pi}{24}$ and angle A is $\frac{\pi}{24}$, we know that angle C is $\pi - \left(\frac{13 \pi}{24} + \frac{\pi}{24}\right) = \frac{10 \pi}{24} = \frac{5 \pi}{12}$

Given $a = 8$, $b = 3$, and $C = \frac{5 \pi}{12}$, we can calculate the area using $\frac{1}{2} a b \sin \left(C\right)$:

Area = $\frac{1}{2} \left(3\right) \left(8\right) \sin \left(\frac{5 \pi}{12}\right)$

$\approx 11.591$