Two corners of a triangle have angles of #(3 pi ) / 8 # and # pi / 4 #. If one side of the triangle has a length of #4 #, what is the longest possible perimeter of the triangle?

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Answer 1 · 2017-12-11T06:00:40

Longest possible perimeter of the triangle is 14.4526

Given are the two angles #(pi)/4# and #(3pi)/8# and the length 1

The remaining angle:

#= pi - (((pi)/4) + (3pi)/8) = (3pi)/8#

I am assuming that length AB (4) is opposite the smallest angle

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

#4 / sin ((pi)/4) = b / sin ((3pi) /8) = c / ((3pi) / 8)#

#b = (4*sin((3pi)/8)) / sin ((pi) /4) = 5.2263#

#c = (4*sin ((3pi)/8)) / sin ((pi)/4) = 5.2263#

Longest possible perimeter of the triangle is =# (a+b+c) = (4+5.2263+5.2263) = 14.4526#