# A triangle has sides A, B, and C. Sides A and B have lengths of 10 and 4, respectively. The angle between A and C is (7pi)/24 and the angle between B and C is  (pi)/8. What is the area of the triangle?

May 14, 2018

$A = 19.31851653 c {m}^{2}$

#### Explanation:

$\frac{7 \pi}{24} + \frac{\pi}{8} = \frac{7 \pi}{24} + \frac{3 \pi}{24} = \frac{10 \pi}{24}$

The angle at C is $\frac{24 \pi}{24} - \frac{10 \pi}{24} = \frac{14 \pi}{24}$

Area of the triangle is $\frac{1}{2} \times a \times b \times \sin C$

A=$\frac{1}{2} \times 10 \times 4 \times \sin \left[\frac{14 \pi}{24}\right]$

A=19.31851653