A triangle has two corners with angles of # pi / 12 # and # (5 pi )/ 8 #. If one side of the triangle has a length of #8 #, what is the largest possible area of the triangle?

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Answer 1 · 2017-12-08T14:44:42

Largest possible area of the triangle is 90.6224

Given are the two angles #(pi)/12# and #(5pi)/8# and the length 8

The remaining angle:

#= pi - ((pi)/12) + (5pi)/8) = (7pi)/24#

I am assuming that length AB (8) is opposite the smallest angle.

Using the ASA

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

Area#=( 8^2*sin((7pi)/24)*sin((5pi)/8))/(2*sin(pi/12))#

Area#=90.6224#