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

Mar 27, 2018

color(blue)(Delta " " A_t = (1/2) a b sin C = (1/2) * 5 * 7 * sin ((5pi)/8) = 16.17

#### Explanation:

$a = 5 , b = 7 , \hat{A} = \frac{\pi}{8} , \hat{B} = \frac{\pi}{4}$

To find the area of the triangle.

$\hat{C} = \pi - \frac{\pi}{8} - \frac{\pi}{4} = \frac{5 \pi}{8}$

$\Delta \text{ " A_t = (1/2) a b sin C = (1/2) * 5 * 7 * sin ((5pi)/8) = 16.17 " sq units}$