Two corners of a triangle have angles of # ( pi )/ 3 # and # ( pi ) / 4 #. If one side of the triangle has a length of # 1 #, what is the longest possible perimeter of the triangle?

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Answer 1 · 2017-12-08T15:07:34

Largest possible area of the triangle is 0.7888

Given are the two angles #(pi)/3# and #pi/4# and the length 1

The remaining angle:

#= pi - ((pi)/4) + pi/3) = (5pi)/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#=( 1^2*sin(pi/3)*sin((5pi)/12))/(2*sin(pi/4))#

Area#=0.7888#