# A triangle has sides A, B, and C. Sides A and B have lengths of 12 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?

Oct 21, 2016

$A r e a = 36 u n i t {s}^{2}$

#### Explanation:

Given:
side $a = 12$
side $b = 6$
$\angle B = \frac{7 \pi}{24}$
$\angle A = 5 \frac{\pi}{24}$

Because A and B sum to $\frac{\pi}{2}$, $\angle C = \frac{\pi}{2}$ and this is a right triangle with sides a and b as the base and height.

$A r e a = \frac{1}{2} \left(12\right) \left(6\right)$

$A r e a = 36 u n i t {s}^{2}$