# 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 6, what is the area of the triangle?

Feb 17, 2018

Area A_t =/(1/2) 6 * 6 * sin ((5pi)/6) = color(red)(9

#### Explanation:

$\hat{A} = \frac{\pi}{12} , \hat{C} = \frac{5 \pi}{6} , b = 6$

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

$\hat{A} = \hat{B} , \therefore a = b = 6$ (isosceles triangle)

Area A_t =/(1/2) 6 * 6 * sin ((5pi)/6) = color(red)(9