Two corners of a triangle have angles of # (5 pi )/ 12 # 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 · 2017-12-08T12:32:03

Largest possible area of the triangle is 21.2942

Given are the two angles #(5pi)/12# and #pi/3# and the length 6

The remaining angle:

#= pi - (((5pi)/12) + pi/3) = pi/4#

I am assuming that length AB (6) 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((5pi)/12))/(2*sin(pi/4))#

Area#=21.2942#