# A triangle has sides A, B, and C. The angle between sides A and B is (3pi)/4 and the angle between sides B and C is pi/12. If side B has a length of 12, what is the area of the triangle?

Jun 10, 2018

color(maroon)("Area of " Delta = 26.35 " sq units"

#### Explanation:

$\hat{A} = \frac{\pi}{12} , \hat{C} = \frac{3 \pi}{4} , \hat{B} = \frac{\pi}{6} , b = 12$

To find Area of the triangle.

Applying the Law of Sines,

$a = \frac{b \cdot \sin A}{\sin} B = \frac{12 \cdot \sin \left(\frac{\pi}{12}\right)}{\sin} \left(\frac{\pi}{6}\right) = 6.21$

$\text{Area of } \Delta = \left(\frac{1}{2}\right) a b \sin C = \left(\frac{1}{2}\right) \cdot 12 \cdot 6.21 \cdot \sin \left(\frac{3 \pi}{4}\right)$

color(maroon)("Area of " Delta = 26.35 " sq units"