Two corners of a triangle have angles of #(7 pi ) / 12 # and # (3 pi ) / 8 #. If one side of the triangle has a length of #8 #, what is the longest possible perimeter of the triangle?

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Answer 1 · 2017-12-08T13:54:35

Largest possible area of the triangle is 218.7819

Given are the two angles #(7pi)/12# and #(3pi)/8# and the length 8

The remaining angle:

#= pi - (((7pi)/12) + (3pi)/8) = pi/24#

I am assuming that length AB (8) is opposite the smallest angle.

Using the ASA

Area#=(c^2*sin(A)*sin(B))/(2*sin(C)#

Area#=( 8^2*sin((3pi)/8)*sin((7pi)/12))/(2*sin(pi/24))#

Area#=218.7819#