Two corners of a triangle have angles of (5 pi )/ 12 and ( pi ) / 12 . If one side of the triangle has a length of 2 , what is the longest possible perimeter of the triangle?

1 Answer
Dec 8, 2017

Longest possible perimeter = 17.1915

Explanation:

Sum of the angles of a triangle =pi

Two angles are (5pi)/12, pi/12
Hence 3^(rd) angle is pi - ((5pi)/12 + pi/12) = (pi)/2

We know a/sin a = b/sin b = c/sin c

To get the longest perimeter, length 2 must be opposite to angle pi/24

:. 2/ sin(pi/12) = b/ sin((5pi)/12) = c / sin ((pi)/2)

b = (2 sin((5pi)/12))/sin (pi/12) = 7.4641

c =( 2* sin((pi)/2))/ sin (pi/12) = 7.7274

Hence perimeter = a + b + c = 2 + 7.4641 + 7.7274 = 17.1915