Two corners of a triangle have angles of # (5 pi )/ 12 # and # pi / 6 #. If one side of the triangle has a length of 12, what is the longest possible perimeter of the triangle?

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Answer 1 · 2017-12-08T14:05:32

Largest possible area of the triangle is 134.3538

Given are the two angles #(5pi)/12# and #pi/6# and the length 12

The remaining angle:

#= pi - (((5pi)/12) + pi/6) = (5pi)/12#

I am assuming that length AB (12) is opposite the smallest angle.

Using the ASA

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

Area#=( 12^2*sin((5pi)/12)*sin((5pi)/12))/(2*sin(pi/6))#

Area#=134.3538#