Two corners of a triangle have angles of # (5 pi )/ 12 # and # (3 pi ) / 8 #. If one side of the triangle has a length of # 1 #, what is the longest possible perimeter of the triangle?

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Answer 1 · 2017-12-08T15:27:09

Longest possible perimeter of the triangle is 4.1043

Given are the two angles #(5pi)/12# and #(3pi)/8# and the length 1

The remaining angle:

#= pi - (((5pi)/12) + (3pi)/8) = (5pi)/24#

I am assuming that length AB (1) is opposite the smallest angle

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

#1 / sin ((5pi)/24) = b / sin ((3pi) /8) = c / ((5pi) / 12)#

#b = (1*sin((3pi)/8)) / sin ((5pi) /24) = 1.5176#

#c = (1*sin ((5pi)/12)) / sin ((5pi)/24) = 1.5867#

Longest possible perimeter of the triangle is =# (a+b+c) = (1+1.5176+1.5867) = 4.1043#