# A triangle has sides A, B, and C. If the angle between sides A and B is (pi)/8, the angle between sides B and C is (5pi)/12, and the length of B is 1, what is the area of the triangle?

Feb 25, 2017

1.23

#### Explanation:

For sake of easy calculations, the angle measures in degrees would be $\angle A = {75}^{o} , \angle B = {22.5}^{o} \mathmr{and} \angle C = {82.5}^{0}$ as shown in the figure below

Now using $\sin \frac{A}{a} = \sin \frac{B}{b} = \sin \frac{C}{c}$, it would be

$\sin \frac{75}{a} = \sin \frac{22.5}{1} = \sin \frac{82.5}{c}$

Thus $a = \sin \frac{75}{\sin} 22.5 = 2.52$; $c = \sin \frac{82.5}{\sin} 22.5 = 2.59$

Now for using Heron formula for the area of a triangle, $s = \frac{2.52 + 1 + 2.59}{2} = \frac{6.11}{2} = 3.05$

(s-a)= 0.53, (s-b)= 2.05, and (s-c)= 0.46

Area of Triangle would be= $\sqrt{3.05 \left(0.53\right) \left(2.05\right) \left(0.46\right)} = 1.23$