Two corners of a triangle have angles of (5 pi )/ 8 and ( pi ) / 6 . If one side of the triangle has a length of 12 , what is the longest possible perimeter of the triangle?

1 Answer
Jun 2, 2018

Longest possible perimeter of the triangle

color(maroon)(P = a + b + c = 48.78

Explanation:

hat A = (5pi)/8, hat B = pi/6, hat C = pi - (5pi)/8 - pi/6 = (5pi)/24

To get the longest perimeter, side 12 should correspond to the least angle hat B = pi/6

Applying the law of Sines,

a = (b * sin A) / sin B = (12 sin ((5pi)/8))/sin (pi/6) = 22.17

c = (sin C * b) / sin B = (12 * sin ((5pi)/24))/sin (pi/6) = 14.61

Longest possible perimeter of the triangle

color(maroon)(P = a + b + c = 22.17+ 12 + 14.61 = 48.78