# A triangle has sides A, B, and C. Sides A and B have lengths of 5 and 12, respectively. The angle between A and C is (11pi)/24 and the angle between B and C is  (pi)/8. What is the area of the triangle?

Feb 21, 2016

≈ 29 square units

#### Explanation:

The area of the triangle can be found by using $\frac{1}{2} A B \sin \theta$
where $\theta \text{ is the angle between A and B }$

The sum of the 3 angles in a triangle is $\pi$

The angle between A and B = $\pi - \left(\frac{11 \pi}{24} + \frac{\pi}{8}\right)$

$= \pi - \frac{14 \pi}{24} = \frac{5 \pi}{12}$

area = 1/2xx5xx12xxsin((5pi)/12) ≈ 29" square units"