Two corners of a triangle have angles of ( pi )/ 3 and ( pi ) / 4 . If one side of the triangle has a length of 8 , what is the longest possible perimeter of the triangle?

1 Answer
Oct 19, 2017

Longest possible perimeter = 28.726

Explanation:

Three angles are pi/3, pi/4, (5pi)/12
To get longest perimeter, equate side 8 to the least angle.

8/sin (pi/4) = b/ sin (pi/3) = c/ sin ((5pi)/12)

b = (8* sin(pi/3))/sin (pi/4) = (8*(sqrt3/2))/(1/sqrt2)
b = 8sqrt(3/2) = 9.798

c = (8*sin(5pi)/(12)) / sin (pi/4) = 8sqrt2*sin((5pi)/12) = 10.928

Longest perimeter possible = 8 + 9.798 + 10.928 = 28.726