Two corners of a triangle have angles of #(3 pi ) / 8 # and # pi / 8 #. If one side of the triangle has a length of #2 #, what is the longest possible perimeter of the triangle?

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Answer 1 · 2017-12-21T08:36:09

Largest possible area of triangle 9.0741

Given #: /_ A = pi /8 /_B = (3pi)/8#

# /_C = (pi - pi /8 - (3pi)/8 ) = (pi)/2 #

To get the longest perimeter, we should consider the side corresponding to the angle that is the smallest.

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

#2 / sin (pi/8) = b / sin ((3pi)/8) = c / sin ((pi)/2)#

#:. b = (2 * sin ((3pi)/8)) / sin (pi/8) = 1.8478#

#c = (2 * sin (pi/2)) / sin (pi/8) = 5.2263#

Longest possible perimeter #P = 2 + 1.8478 + 5.2263 = 9.0741#