# A triangle has sides A, B, and C. The angle between sides A and B is (5pi)/6 and the angle between sides B and C is pi/12. If side B has a length of 9, what is the area of the triangle?

Jun 10, 2018

color(crimson)("Area of " Delta = 20.25 " sq units"

#### Explanation:

$\hat{A} = \frac{\pi}{12} , \hat{C} = \frac{5 \pi}{6} , \hat{B} = \frac{\pi}{12} , b = 9$

color(blue)("As angles " hat A , hat B " are equal, their sides will also be equal "

color(blue)(" and the " Delta " is isosceles"

$\therefore a = b = 9$

$\text{Area of } \Delta = \left(\frac{1}{2}\right) a b \sin C = \left(\frac{1}{2}\right) \cdot {9}^{2} \cdot \sin \left(\frac{5 \pi}{6}\right)$

color(crimson)("Area of " Delta = 20.25 " sq units"