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 (5pi)/8 and the angle between B and C is  (5pi)/24. What is the area of the triangle?

Mar 27, 2018

color(purple)(A_t = (1/2) a b sin C = 8.75 " sq units"

Explanation:

$a = 5 , b = 7 , \hat{A} = \frac{5 \pi}{24} , \hat{B} = \frac{5 \pi}{8}$

To find the area of the triangle ${A}_{t}$

$\hat{C} = \pi - \frac{5 \pi}{24} - \frac{5 \pi}{8} = \frac{\pi}{6}$

color(purple)(A_t = (1/2) a b sin C = (1/2) * 5 * 7 * sin (pi/6) = 8.75