Two corners of a triangle have angles of #(3 pi ) / 8 # and # pi / 3 #. If one side of the triangle has a length of #6 #, what is the longest possible perimeter of the triangle?

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Answer 1 · 2017-12-08T12:40:33

Largest possible area of the triangle is 18.1531

Given are the two angles #(3pi)/8# and #pi/3# and the length 6

The remaining angle:

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

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

Using the ASA

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

Area#=( 6^2*sin(pi/3)*sin((3pi)/8))/(2*sin((7pi)/24)#

Area#=18.1531#