A triangle has two corners with angles of # pi / 12 # and # pi / 8 #. If one side of the triangle has a length of #16 #, what is the largest possible area of the triangle?

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Answer 1 · 2017-12-11T07:09:18

Largest possible area of the triangle is 115.2127

Given are the two angles #(pi)/8# and #pi/8# and the length 1

The remaining angle:

#= pi - ((pi)/12) + pi/8) = (19pi)/24#

I am assuming that length AB (12) is opposite the smallest angle.

Using the ASA

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

Area#=( 16^2*sin((19pi)/24)*sin((pi)/8))/(2*sin(pi/12))#

Area#=115.2127#