Question

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?

Answer 1

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`