# A triangle has sides A, B, and C. Sides A and B have lengths of 2 and 3, respectively. The angle between A and C is (5pi)/24 and the angle between B and C is  (11pi)/24. What is the area of the triangle?

Mar 27, 2018

color(green)(A_t = 2.6 " sq units"

#### Explanation:

$\hat{A} = \frac{11 \pi}{24} , \hat{B} = \frac{5 \pi}{24} , a = 2 , b = 3$

$\hat{C} = \pi - \hat{A} - \hat{B} = \pi - \frac{11 \pi}{24} - \frac{5 \pi}{24} = \frac{\pi}{3}$

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

${A}_{t} = \left(\frac{1}{2}\right) \cdot 2 \cdot 3 \cdot \sin \left(\frac{\pi}{3}\right) = 2.6 \text{ sq units}$