# A triangle has sides A, B, and C. If the angle between sides A and B is (pi)/8, the angle between sides B and C is (7pi)/12, and the length of B is 12, what is the area of the triangle?

Feb 17, 2018

Area of triangle

${A}_{t} = \left(\frac{1}{2}\right) a b \sin C = 33.5467$

#### Explanation:

$\hat{A} = \frac{7 \pi}{12} , \hat{C} = \frac{\pi}{8} , b = 12$

$\hat{B} = \pi - \frac{7 \pi}{12} - \frac{\pi}{8} = \frac{7 \pi}{24}$

$a = \frac{12 \cdot \sin \left(\frac{7 \pi}{12}\right)}{\sin} \left(\frac{7 \pi}{24}\right) = 14.6103$

Area of triangle

${A}_{t} = \left(\frac{1}{2}\right) a b \sin C = \left(\frac{1}{2}\right) \cdot 14.6103 \cdot 12 \cdot \sin \left(\frac{\pi}{8}\right) = 33.5467$