A triangle has two corners with angles of # pi / 4 # and # pi / 6 #. 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 · 2017-12-11T05:14:59

Largest possible area of the triangle is 98.3538

Given are the two angles #(pi)/4# and #pi/6# and the length 1

The remaining angle:

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

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

Area#=98.3538#