A triangle has two corners with angles of # (3 pi ) / 4 # and # ( pi )/ 12 #. If one side of the triangle has a length of #2 #, what is the largest possible area of the triangle?

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Answer 1 · 2017-12-05T12:53:26

Largest possible area of the #Delta = color (purple)(2.7321)#

Given are the two angles #(3pi)/4, pi/12# and the length 2

The remaining angle:

#pi - ((3pi)/4+ pi/12) = (pi)/6#

I am assuming that length AB (2) is opposite the smallest angle.

Using the ASA

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

Area#=( 2^2*sin((3pi)/4)*sin((pi)/6))/(2*sin(pi/12))#

Area#=2.7321#