# 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 19, what is the area of the triangle?

Jun 10, 2018

color(green)("Area of " Delta = 90.25 " sq units"

#### Explanation:

$\hat{A} = \frac{\pi}{12} , \hat{C} \frac{5 \pi}{6} , b = 19 , \hat{B} = \frac{\pi}{12}$

Given triangle is isosceles and sides b & a are equal as both the angles are equal.

$a = b = 19$

$\text{Area of the } \Delta = \left(\frac{1}{2}\right) a b \sin C = \left(\frac{1}{2}\right) \cdot {19}^{2} \cdot \sin \left(\frac{5 \pi}{6}\right)$

color(green)("Area of " Delta = 90.25 " sq units"