# A triangle has sides A, B, and C. The angle between sides A and B is (5pi)/6 and the angle between sides B and C is pi/12. If side B has a length of 2, what is the area of the triangle?

Feb 17, 2018

Area of triangle color(blue)(A_t = (1/2) a b sin C = 1

#### Explanation:

$G i v e n : b = 2 , \hat{A} = \frac{\pi}{12} , \hat{C} = \frac{5 \pi}{6}$

$\hat{B} = \pi - \frac{\pi}{12} - \frac{5 \pi}{6} = \frac{\pi}{12}$

It’s an isosceles triangle with $\hat{A} = \hat{B}$

$\therefore b = a = 2$

Area of triangle ${A}_{t} = \left(\frac{1}{2}\right) a b \sin C = \left(\frac{1}{2}\right) \cdot 2 \cdot 2 \cdot \sin \left(\frac{5 \pi}{6}\right) = \textcolor{b l u e}{1}$