Two corners of a triangle have angles of #pi / 8 # and # pi / 6 #. If one side of the triangle has a length of #7 #, what is the longest possible perimeter of the triangle?

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Answer 1 · 2017-12-11T06:07:35

Longest possible perimeter of the triangle is 31.0412

Given are the two angles #(pi)/6# and #(pi)/8# and the length 1

The remaining angle:

#= pi - (((pi)/6) + (p)/8) = (17pi)/24#

I am assuming that length AB (7) is opposite the smallest angle

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

#7 / sin ((pi)/6) = b / sin ((pi) /8) = c / ((17pi) / 24)#

#b = (7*sin((3pi)/8)) / sin ((pi) /6) = 12.9343#

#c = (7*sin ((17pi)/24)) / sin ((pi)/6) = 11.1069#

Longest possible perimeter of the triangle is =# (a+b+c) = (7+12.9343+11.1069) = 31.0412#