Two corners of a triangle have angles of (5 pi )/ 12 and (3 pi ) / 8 . If one side of the triangle has a length of 1 , what is the longest possible perimeter of the triangle?

1 Answer
Dec 8, 2017

Longest possible perimeter of the triangle is 4.1043

Explanation:

Given are the two angles (5pi)/12 and (3pi)/8 and the length 1

The remaining angle:

= pi - (((5pi)/12) + (3pi)/8) = (5pi)/24

I am assuming that length AB (1) is opposite the smallest angle

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

1 / sin ((5pi)/24) = b / sin ((3pi) /8) = c / ((5pi) / 12)

b = (1*sin((3pi)/8)) / sin ((5pi) /24) = 1.5176

c = (1*sin ((5pi)/12)) / sin ((5pi)/24) = 1.5867

Longest possible perimeter of the triangle is = (a+b+c) = (1+1.5176+1.5867) = 4.1043