Question

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 `9`, what is the longest possible perimeter of the triangle?

Answer 1

Longest possible Perimeter = 36.9372

Explanation:

Three angles of the triangle are `(5pi)/12, (3pi)/8 & (5pi)/24` as the sum of three angles is `pi`
We know `A/sin a=B/sin b=C/sin c`

To get the largest perimeter, we must use the side `9` as opposite to the smallest angle.
`:.A/sin((5pi)/12)=B/sin ((3pi)/8)=9/sin ((5pi)/24)`

`A=(9*sin ((5pi)/12))/sin ((5pi)/24)`
`A ~~ (9*0.9659)/0.6088~~14.2791`

`B=(9*sin ((3pi)/8))/sin ((5pi)/24)`
`B~~(9*0.9239)/0.6088~~13.6581`

Longest Perimeter `9+14.2791+13.6581=36.9372`