# A triangle has sides A, B, and C. Sides A and B have lengths of 4 and 5, respectively. The angle between A and C is (7pi)/8 and the angle between B and C is  (pi)/12. What is the area of the triangle?

Jul 20, 2017

$\text{area " ~~1.305" square units}$

#### Explanation:

$\text{the area ( A) of the triangle is calculated using}$

•color(white)(x)A=1/2ABsinC

$\text{where " C" is the angle between A and B}$

$\Rightarrow \angle C = \pi - \left(\frac{7 \pi}{8} + \frac{\pi}{12}\right) = \frac{\pi}{24}$

$\Rightarrow A = \frac{1}{2} \times 4 \times 5 \times \sin \left(\frac{\pi}{24}\right)$

$\textcolor{w h i t e}{\Rightarrow A} \approx 1.305 \text{ square units}$