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

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Answer 1 · 2017-12-11T07:03:45

Largest possible area of the triangle is 170.3538

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

The remaining angle:

#= pi - ((pi)/4) + pi/12) = (2pi)/3#

I am assuming that length AB (12) is opposite the smallest angle.

Using the ASA

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

Area#=( 12^2*sin((pi)/4)*sin((2pi)/3))/(2*sin(pi/12))#

Area#=170.3538#