Two corners of a triangle have angles of # (5 pi )/ 12 # and # pi / 4 #. If one side of the triangle has a length of 9, what is the longest possible perimeter of the triangle?

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Answer 1 · 2018-06-01T15:30:00

Longest possible perimeter #color(crimson)(P = 33.21#

#hat A = (5pi)/12, hat B = pi/4, hat C = pi/3#

Least angle #pi/4# should correspond to the side of length 9.

Applying Law of Sines,

#a / sin A = b / sin B = c / sin C#

#a = (b sin A) / sin B = (9 * sin ((5pi)/12)) / sin (pi/4) = 12.29#

#c = (9 sin(pi/3)) / sin(pi/4) = 12.02#

Longest possible perimeter #P = 9 + 12.29 + 12.02 = 33.21#