# Two corners of a triangle have angles of  (5 pi )/ 12  and  ( pi ) / 12 . If one side of the triangle has a length of  5 , what is the longest possible perimeter of the triangle?

Aug 16, 2016

$= 11.12$

#### Explanation:

Clearly this is a right angled triangle as $\pi - \frac{5 \pi}{12} - \frac{\pi}{12} = \frac{\pi}{2}$
One $s i \mathrm{de} = h y p o t e n u s e = 5$ ;So other sides $= 5 \sin \left(\frac{\pi}{12}\right) \mathmr{and} 5 \cos \left(\frac{\pi}{12}\right)$

Therefore Perimeter of the triangle$= 5 + 5 \sin \left(\frac{\pi}{12}\right) + 5 \cos \left(\frac{\pi}{12}\right)$

$= 5 + \left(5 \times 0.2588\right) + \left(5 \times 0.966\right)$

=5+1.3+4.83)

$= 11.12$