# 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 1, what is the area of the triangle?

Jul 3, 2018

color(magenta)("Area of Triangle " A_t = 1.183

#### Explanation:

$\hat{A} = \frac{\pi}{12} , \hat{C} = \frac{\pi}{4} , \hat{B} = \frac{2 \pi}{3} , b = 1$

As per Law of sines,

$a = \frac{b \cdot \sin A}{\sin} B = \frac{1 \cdot \sin \left(\frac{2 \pi}{3}\right)}{\sin} \left(\frac{\pi}{12}\right)$

$a = 3.346$

$\text{Area of Triangle } {A}_{t} = \left(\frac{1}{2}\right) a b \sin C$

${A}_{t} = \left(\frac{1}{2}\right) \cdot 3.346 \cdot 1 \cdot \sin \left(\frac{\pi}{4}\right) = 1.183$