A triangle has two corners with angles of # ( pi ) / 4 # and # ( 7 pi )/ 12 #. If one side of the triangle has a length of #1 #, what is the largest possible area of the triangle?

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Answer 1 · 2017-12-08T10:09:09

Largest possible area = 0.683

Given are the two angles #(7pi)/12# and #pi/4# and the length 1

The remaining angle:

#= pi - (((7pi)/12) + pi/4) = pi/6#

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/4)*sin((7pi)/12))/(2*sin(pi/6))#

Area#=0.683