# A triangle has sides A, B, and C. Sides A and B have lengths of 5 and 8, respectively. The angle between A and C is (13pi)/24 and the angle between B and C is  (3pi)/8. What is the area of the triangle?

Mar 27, 2018

${A}_{t} = \left(\frac{1}{2}\right) \cdot a \cdot b \cdot \sin C = 5.18 \text{ sq units}$

#### Explanation:

$\hat{B} = \frac{13 \pi}{24} , \hat{A} = \frac{3 \pi}{8} , a = 5 , b = 8$

To find the area of the triangle.

$\hat{C} = \pi - \hat{A} - \hat{B} = \pi - \frac{3 \pi}{8} - \frac{13 \pi}{24} = \frac{\pi}{12}$

$\text{Area of triangle } = {A}_{t} = \left(\frac{1}{2}\right) \cdot a \cdot b \cdot \sin C$

${A}_{t} = \left(\frac{1}{2}\right) \cdot 5 \cdot 8 \cdot \sin \left(\frac{\pi}{12}\right) = 5.18 \text{ sq units}$