# A triangle has sides A, B, and C. The angle between sides A and B is (pi)/2 and the angle between sides B and C is pi/12. If side B has a length of 15, what is the area of the triangle?

Aug 7, 2016

$= 30$

#### Explanation:

This is a right angled triangle where $B = 15$
Therefore
Angle between $A$ and $C$ is $\pi - \left(\frac{\pi}{2} + \frac{\pi}{12}\right) = 5 \frac{\pi}{12}$
$\frac{A}{\sin} \left(\frac{\pi}{12}\right) = \frac{B}{\sin} \left(5 \frac{\pi}{12}\right)$
or
$\frac{A}{\sin} \left(\frac{\pi}{12}\right) = \frac{15}{\sin} \left(5 \frac{\pi}{12}\right)$
or
$A = \frac{15}{\sin} \left(5 \frac{\pi}{12}\right) \left(\sin \frac{\pi}{12}\right)$
or
$A = 15 \left(0.268\right)$
or
$A = 4$
Therefore
Area of the triangle$= \frac{1}{2} \left(15\right) \left(4\right)$
$= \frac{60}{2}$
$= 30$