Question

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

Answer 1

Longest possible perimeter `= 142.9052`

Explanation:

Three angles are `pi/3, (5pi )/ 8, (pi - (pi/3+(5pi)/8)`
=`pi/3, (5pi)/8, pi/24)`

To get longest possible perimeter, length 12 should correspond to least angle `pi/24`
`:. 12/sin (pi/24) = b / sin ((5pi)/8) = c / sin (pi/3)`

`c = (12* sin(pi/3)) / sin (pi/24) = 45.9678`
`b = (12 * (sin (5pi)/8))/sin (pi/24) = 84.9374`

Perimeter `= 12 + 45.9678 + 84.9374 = 142.9052`