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

Answer 1

Longest possible perimeter = 29.426

Explanation:

Sum of the angles of a triangle `=pi`

Two angles are `(5pi)/8, pi/3`
Hence `3^(rd)`angle is `pi - ((5pi)/8 + pi/3) = pi/24`

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

To get the longest perimeter, length 2 must be opposite to angle `pi/24`

`:. 2/ sin(pi/24) = b/ sin((5pi)/8) = c / sin (pi/3)`

`b = (2sin((5pi)/8))/sin (pi/24) = 14.1562`

`c =( 2* sin(pi/3))/ sin (pi/24) = 13.2698`

Hence perimeter `= a + b + c = 2 + 14.1562 + 13.2698 = 29.426`