# A triangle has sides A, B, and C. The angle between sides A and B is (7pi)/12 and the angle between sides B and C is pi/12. If side B has a length of 19, what is the area of the triangle?

Feb 17, 2018

a = (1/2) a b sin C ~~ color(purple)(5.6783

#### Explanation:

$\hat{C} = \frac{7 \pi}{12} , \hat{A} = \frac{\pi}{12} , b = 19$

$\hat{B} = \pi - \frac{\pi}{12} - \frac{7 \pi}{12} = \frac{\pi}{3}$

$\frac{a}{\sin} A = \frac{b}{\sin} B$

a = (1/2) a b sin C = (19 * sin (pi/12)) / sin(pi/3) ~~ color(purple)(5.6783