# A triangle has sides A, B, and C. The angle between sides A and B is pi/6 and the angle between sides B and C is pi/12. If side B has a length of 14, what is the area of the triangle?

Feb 17, 2018

Area of Delta ABC = (1/2) a b sin C = color(green)(17.9352

#### Explanation:

$\hat{A} = \frac{\pi}{12} , C = \frac{\pi}{6} , b = 14$

$\hat{B} = \pi - \frac{\pi}{12} - \frac{\pi}{6} = \frac{3 \pi}{4}$

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

$a = \frac{14 \cdot \sin \left(\frac{\pi}{12}\right)}{\sin} \left(\frac{3 \pi}{4}\right) = 5.1244$

Area of Delta ABC = (1/2) a b sin C = 0.5 * 5.1244 * 14 * sin (pi/6) = color(green)(17.9352