Two corners of a triangle have angles of #pi / 3 # and # pi / 12 #. 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 · 2017-12-08T12:45:08

Largest possible area of the triangle is 103.4256

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

The remaining angle:

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

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

Area#=103.4256#