# A triangle has sides A, B, and C. Sides A and B have lengths of 2 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 26, 2018

color(red)("Area of the triangle " A_t = 3.5 " sq units"

#### Explanation:

$a = 2 , \hat{A} = \frac{5 \pi}{24} , b = 7 , \hat{B} = \frac{5 \pi}{8}$

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

We know now two sides and the included angle.

We will use the formula ${A}_{t} = \left(\frac{1}{2}\right) a b \sin C$

${A}_{t} = \left(\frac{1}{2}\right) \cdot 2 \cdot 7 \cdot \sin \left(\frac{\pi}{6}\right) = 3.5 \text{ sq units}$