# A triangle has sides A,B, and C. If the angle between sides A and B is (7pi)/8, the angle between sides B and C is pi/12, and the length of B is 1, what is the area of the triangle?

Mar 10, 2017

Area of the triangle is $0.3794$

#### Explanation:

As two angles are $\frac{7 \pi}{8}$ and $\frac{\pi}{12}$,

third angle between sides A and C is $\pi - \frac{7 \pi}{8} - \frac{\pi}{12} = \frac{\pi}{24}$

Now using sine formula for triangles, we have

$\frac{A}{\sin} \left(\frac{\pi}{12}\right) = \frac{C}{\sin} \left(\frac{7 \pi}{8}\right) = \frac{B}{\sin} \left(\frac{\pi}{24}\right)$ and as $B = 1$

we have $\frac{A}{0.25882} = \frac{C}{0.38268} = \frac{1}{0.13053} = 7.661$

Hence $A = 7.6611 \times 0.25882 = 1.983$ and

$C = 7.6611 \times 0.38268 = 2.932$

As area of a triangle is given by $\frac{1}{2} b c \sin A$

Area of the triangle is $\frac{1}{2} \times 1 \times 2.932 \times 0.25882 = 0.3794$