# 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 1, what is the area of the triangle?

Feb 17, 2018

Area of $\Delta$ ${A}_{t} = \left(\frac{1}{2}\right) a b \sin C = 0.183$

#### Explanation:

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

$\hat{B} = \pi - \frac{\pi}{12} - \frac{3 \pi}{4} = \frac{\pi}{6}$

$\frac{a}{\sin} A = \frac{b}{\sin} B$

a = ((1 * sin (pi/12)) / sin (pi/6) = 0.5176

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

${A}_{t} = \left(\frac{1}{2}\right) 0.5176 \cdot 1 \sin \left(\frac{3 \pi}{4}\right) = 0.183$