Question

Two corners of a triangle have angles of `(7 pi )/ 12` and `(3 pi ) / 8`. If one side of the triangle has a length of `15`, what is the longest possible perimeter of the triangle?

Answer 1

Largest possible perimeter 232.1754

Explanation:

Given two angles are `(7pi)/12, (3pi)/8`
Third angle `= (pi - ((7pi)/12 - (3pi)/8) = pi/24`

We know`a/sin a = b/sin b = c/sin c`

To get the longest perimeter, length 15 must be opposite to angle `pi/24`

`:. 15/ sin(pi/24) = b/ sin((7pi)/12) = c / sin ((3pi)/8)`

`b = (15 sin((7pi)/12))/sin (pi/24) = 111.0037`

`c =( 15 sin((3pi)/8))/ sin (pi/24) = 106.1717`

Hence perimeter `= a + b + c = 5 + 111.0037 + 106.1717 = 232.1754`