# A triangle has sides A, B, and C. Sides A and B have lengths of 8 and 7, respectively. The angle between A and C is (17pi)/24 and the angle between B and C is  (5pi)/24. What is the area of the triangle?

Mar 27, 2018

color(blue)(A_t = (1/2) * a * b * sin C = 7.25 " sq units"

#### Explanation:

$a = 8 , b = 7 , \hat{A} = \frac{5 \pi}{24} , \hat{B} = \frac{17 \pi}{24}$

$\text{Sum of the three angles of a triangle } = {\pi}^{c}$

$\hat{C} = \pi - \hat{A} - \hat{B} = \pi - \frac{5 \pi}{24} - \frac{17 \pi}{24} = \frac{\pi}{12}$

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

color(blue)(A_t = (1/2) * 8 * 7 * sin (pi/12) = 7.25 " sq units"