Two corners of a triangle have angles of #(7 pi ) / 12 # and # pi / 12 #. 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 · 2017-12-08T14:58:22

Largest possible area of the triangle is 79.1852

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

The remaining angle:

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

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

Using the ASA

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

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

Area#=79.1852#