Question

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

Answer 1

Longest possible perimeter `color(orange)(P = 1 + 1.22 + 1.37 = 3.59`

Explanation:

`hat A = (5pi)/12, hat B = pi/3, hat C = pi/4`

Side 1 should correspond to `hat C = pi/4` the least angle to get the longest perimeter.

As per Law of Sines, `a / sin A = b / sin B = c / sin C`

`:. a = (sin ((5pi)/12) * 1) / sin (pi/4) = 1.37`

`b = (sin (pi/3) * 1) / sin(pi/4) = 1.22`

Longest possible perimeter `color(orange)(P = 1 + 1.22 + 1.37 = 3.59`