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

Aug 4, 2016

$= 33.62$

#### Explanation:

Since the triangle is isosceles height divides the base equally.
In other words the said triangle consists of 2 right angled triangles with base=$\frac{B}{2} = \frac{6}{2} = 3$ and hypotenuse =Side $A$
Therefore we can write
$A \left(\cos \left(\frac{5 \pi}{12}\right)\right) = 3$
or
$A \left(0.2588\right) = 3$
or
$A = \frac{3}{0.2588}$
or
$A = 11.6$
In a right angled triangle height $h = \sqrt{{11.6}^{2} - {3}^{2}} = 11.21$
Therefore Area of the triangle$= \frac{1}{2} \left(h\right) \left(B\right)$
$= \frac{1}{2} \left(11.21\right) \left(6\right)$
$= \left(11.21\right) \left(3\right)$
$= 33.62$