# 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/12. If side B has a length of 15, what is the area of the triangle?

Aug 11, 2016

$= 28.13$

#### Explanation:

The angle between $A$ and $C$ $= \pi - \left(\frac{5 \pi}{12} + \frac{\pi}{12}\right) = \pi - \frac{\pi}{2} = \frac{\pi}{2}$
This shows that triangle is right-angled with hypotenuse $= B = 15$
Hence $h e i g h t =$side $A = 15 \sin \left(\frac{\pi}{12}\right)$ and $b a s e =$side $B = 15 \cos \left(\frac{\pi}{12}\right)$
Therefore Area of the triangle$= \frac{1}{2} \times h e i g h t \times b a s e$
$= \frac{1}{2} \times 15 \sin \left(\frac{\pi}{12}\right) 15 \cos \left(\frac{\pi}{12}\right)$
$= \frac{225}{2} \left(0.2588\right) \left(0.966\right)$
$= 28.13$