A triangle has two corners with angles of # pi / 12 # and # pi / 6 #. If one side of the triangle has a length of #6 #, what is the largest possible area of the triangle?

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Answer 1 · 2017-12-05T12:36:41

Largest possible area of the #Delta = color (purple)(49.1769)#

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

The remaining angle is #(pi - (pi/12 + pi/6) = (3pi)/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((3pi)/4)*sin(pi/6))/(2*sin(12))#

Area#=color (purple)(49.1769)#