# A triangle has sides A, B, and C. The angle between sides A and B is pi/3 and the angle between sides B and C is pi/12. If side B has a length of 8, what is the area of the triangle?

Feb 17, 2018

A_t = (1/2) a b sin C =color(green)( 7.4256

#### Explanation:

$\hat{A} = \frac{\pi}{12} , \hat{C} = \frac{\pi}{3} , b = 8$

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

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

$a = \frac{8 \cdot \sin \left(\frac{\pi}{12}\right)}{\sin} \left(\frac{7 \pi}{12}\right) = 2.1436$

A_t = (1/2) a b sin C = (1/2) * 2.1436 * 8 sin (pi/3) =color(green)( 7.4256