Question

Two corners of a triangle have angles of `(5 pi )/ 8` and `( pi ) / 6`. If one side of the triangle has a length of `17`, what is the longest possible perimeter of the triangle?

Answer 1

Longest possible perimeter = 69.1099

Explanation:

Three angles are `(5pi)/8, pi/6, (5pi)/24`

To get the longest perimeter, side with length 17 should correspond to least angle of the triangle `(pi/6)`

`17 / sin (pi/6) = b / sin ((5 pi)/8) = c / sin ((5pi)/ 24)`

`b = (17 *sin (( 5 pi)/ 8 ))/sin (pi/6 ) = 31.412`

`c =( 17 * sin ((5 pi )/24))/sin (pi/ 6 ) = 20.698`

Perimeter `= a + b + c = 17 + 31.412 + 20.698 = 69.1099`