# A triangle has sides A, B, and C. If the angle between sides A and B is (pi)/12, the angle between sides B and C is (7pi)/12, and the length of B is 17, what is the area of the triangle?

Jun 3, 2018

Area of triangle color(green)(A_t = 139.57 sq units

#### Explanation:

$\hat{A} = \frac{7 \pi}{12} , \hat{C} = \frac{\pi}{12} , \hat{B} = \frac{\pi}{3} , b = 17$

Applying Law of Sines, $\frac{a}{\sin} A = \frac{b}{\sin} B$

$a = \frac{17 \cdot \sin \left(\frac{7 \pi}{12}\right)}{\sin} \left(\frac{\pi}{3}\right) = 18.96$

Area of triangle ${A}_{t} = \left(\frac{1}{2}\right) a b \sin C$

${A}_{t} = \left(\frac{1}{2}\right) \cdot 18.96 \cdot 17 \cdot \sin \left(\frac{\pi}{12}\right) = 139.57$ sq units