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

Jan 19, 2017

$= 1.675 u n i {t}^{2}$

#### Explanation:

The other angle is $\pi - \frac{\pi}{12} - \frac{\pi}{12} = \frac{10}{12} \pi = \frac{5}{6} \pi$

Since it is an isosceles triangle with 2 equal size of sides,
The height of triangle,$h = \frac{5}{2} \tan \left(\frac{\pi}{12}\right)$
$h = \frac{5}{2} \tan \left(\frac{\pi}{12}\right)$

The area or triangle $= \frac{1}{2} \cdot 5 \cdot h$
$= \frac{1}{2} \cdot 5 \cdot \frac{5}{2} \tan \left(\frac{\pi}{12}\right)$

$= \frac{25}{4} \cdot 0.268$

$= 1.675 u n i {t}^{2}$