# A triangle has sides A, B, and C. The angle between sides A and B is (5pi)/12 and the angle between sides B and C is pi/6. If side B has a length of 1, what is the area of the triangle?

Nov 14, 2016

The area of the triangle is $\frac{1}{4} s q . u n i t$

#### Explanation:

The angle between sides $A \mathmr{and} B$ is $\angle c = \frac{5 \pi}{12} = \frac{5 \cdot 180}{12} = {75}^{0}$.

The angle between sides $B \mathmr{and} C$ is $\angle a = \frac{\pi}{6} = \frac{180}{6} = {30}^{0}$

The angle between sides $A \mathmr{and} C$ is $\angle b = 180 - \left(75 + 30\right) = {75}^{0}$

$\angle b = \angle c = {75}^{0}$. So it is an isocelles triangle , having opposite sides equal. So $B = C = 1$ and their included angle $\angle a = {30}^{0}$

Hence the area of the triangle is ${A}_{t} = \frac{B \cdot C \cdot \sin a}{2} = \frac{1 \cdot 1 \cdot \sin 30}{2} = \frac{1}{4} s q . u n i t$[Ans]