Two corners of a triangle have angles of # (2 pi )/ 3 # and # ( pi ) / 6 #. 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 · 2017-12-08T13:40:46

Largest possible area of the triangle is 21.2176

Given are the two angles #(2pi)/3# and #pi/6# and the length 7

The remaining angle:

#= pi - (((2pi)/3) + pi/6) = pi/6#

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/6)*sin((2pi)/3))/(2*sin(pi/6))#

Area#=21.2176#