# A triangle has sides A, B, and C. Sides A and B have lengths of 5 and 9, respectively. The angle between A and C is (19pi)/24 and the angle between B and C is  (pi)/8. What is the area of the triangle?

Mar 3, 2018

5.8234 unit²

#### Explanation:

Let say a is representing angle for side A, b for side B and c for side C.

The area of triangle $= \frac{1}{2} \cdot A \cdot B \cdot \sin c$.

Angle c is located between side A and B, therefore
$c = \pi - \frac{\pi}{8} - \frac{19}{24} \pi$
$c = \pi - \frac{22}{24} \pi = \frac{2}{24} \pi = \frac{\pi}{12}$

The area of triangle $= \frac{1}{2} \cdot 5 \cdot 9 \cdot \sin \left(\frac{\pi}{12}\right)$

$= \frac{1}{2} \cdot 5 \cdot 9 \cdot 0.2588$
$= 5.8234$ unit²#