# A triangle has sides A, B, and C. The angle between sides A and B is pi/4 and the angle between sides B and C is pi/12. If side B has a length of 35, what is the area of the triangle?

Apr 7, 2018

color(blue)("Area of " Delta " " A_t = 129.44

#### Explanation:

$\hat{B} = \pi - \hat{A} - \hat{C} = \pi - \frac{\pi}{12} - \frac{\pi}{4} = \frac{2 \pi}{3}$

As per the Law of Sines,

$\frac{a}{\sin} A = \frac{b}{\sin} B = \frac{c}{S} \in C$

$a = \frac{35 \cdot \sin \left(\frac{\pi}{12}\right)}{\sin} \left(\frac{2 \pi}{3}\right) = 10.46$

color(green)("Area of Triangle " A_t = (1/2) a b sin C

${A}_{t} = \left(\frac{1}{2}\right) \cdot 10.46 \cdot 35 \cdot \sin \left(\frac{\pi}{4}\right) = 129.44$