# A triangle has sides A, B, and C. Sides A and B have lengths of 11 and 7, respectively. The angle between A and C is (7pi)/24 and the angle between B and C is  (13pi)/24. What is the area of the triangle?

Apr 3, 2018

$\frac{77}{4} u n i t {s}^{2}$

#### Explanation:

$7 \frac{\pi}{24} + 13 \frac{\pi}{24} + \angle B C A = \pi$ (angle sum of triangle)

$\angle B C A = \frac{\pi}{6}$

Area of triangle ABC
= $\frac{1}{2} \times 11 \times 7 \times \sin \left(\frac{\pi}{6}\right)$ ($A r e a = \frac{1}{2} a \times b \times \sin c$)
=$\frac{77}{4} u n i t {s}^{2}$