# A triangle has sides A, B, and C. If the angle between sides A and B is (pi)/6, the angle between sides B and C is (2pi)/3, and the length of side B is 25, what is the area of the triangle?

Apr 10, 2018

:.color(green)(A_t = (1/2) * 25 * 25 * sin ((2pi)/3) = 270.63 " sq units"

#### Explanation:

$\hat{A} = \frac{2 \pi}{3} , \hat{C} = \frac{\pi}{6} , \hat{B} = \pi - \frac{\pi}{6} - \frac{2 \pi}{3} = \frac{\pi}{3} , b = 25$

It's an isosceles triangle with sides b & c equal.

$\therefore c = b = 25$

color(blue)("Area of " Delta " " A_t = (1/2) * b * c * sin A

:.color(green)(A_t = (1/2) * 25 * 25 * sin ((2pi)/3) = 270.63 " sq units"