Two corners of a triangle have angles of (7 pi ) / 12 and (3 pi ) / 8 . If one side of the triangle has a length of 6 , what is the longest possible perimeter of the triangle?

1 Answer
Dec 20, 2017

Longest possible perimeter P = 92.8622

Explanation:

Given : /_ C = (7pi) /12, /_B = (3pi)/8

/_A = (pi - (7pi) /12 - (3pi)/8 ) = pi / 24

To get the longest perimeter, we should consider the side corresponding to the angle that is the smallest.

a / sin A = b / sin B = c / sin C

6 / sin (pi/24) = b / sin ((3pi)/8) = c / sin ((7pi)/12)

:. b = (6 * sin ((3pi)/8)) / sin (pi/24) = 42.4687

c = (6 * sin ((7pi)/12))/sin (pi/24) = 44.4015

Longest possible perimeter P = 6 + 42.4687 + 44.4015 = 92.8622