# A triangle has sides A, B, and C. Sides A and B have lengths of 2 and 3, respectively. The angle between A and C is (5pi)/24 and the angle between B and C is  (3pi)/8. What is the area of the triangle?

Jul 20, 2016

$2.9 s q u n i t$

#### Explanation:

Given

$A , B , C \text{ are three sides of a triangle}$

$A = 2 \mathmr{and} B = 3$

$\text{Angle between A & C} = \left(\frac{5 \pi}{24}\right)$

$\text{Angle between B & C} = \left(\frac{3 \pi}{8}\right)$

$\text{Let Angle between A & B} = \theta$
$= \pi - \frac{3 \pi}{8} - \frac{5 \pi}{24} = \frac{\left(24 - 9 - 5\right) \pi}{24} = \frac{5 \pi}{12}$

$\text{Area of triangle} = \frac{1}{2} \cdot A \cdot B \cdot \sin \theta$

$= \frac{1}{2} \cdot 2 \cdot 3 \cdot \sin \left(\frac{5 \pi}{12}\right) = 2.9 s q u n i t$