A triangle has two corners with angles of # pi / 12 # and # pi / 4 #. If one side of the triangle has a length of #5 #, what is the largest possible area of the triangle?

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Answer 1 · 2017-12-08T13:02:35

Largest possible area of the triangle is 29.5753

Given are the two angles #(pi)/12# and #pi/4# and the length 5

The remaining angle:

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

I am assuming that length AB (5) is opposite the smallest angle.

Using the ASA

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

Area#=( 5^2*sin(pi/4)*sin((2p)/3))/(2*sin(pi/12))#

Area#=29.5753#