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

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Answer 1 · 2017-12-08T10:12:16

Largest possible area of the triangle = 4

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

The remaining angle:

#= pi - (((pi)/12) + pi/12) =( 5pi)/6#

I am assuming that length AB (4) is opposite the smallest angle.

Using the ASA

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

Area#=( 4^2*sin(pi/12)*sin((5pi)/6))/(2*sin(pi/12))#

Area#=4#