A triangle has two corners with angles of # pi / 12 # and # (5 pi )/ 8 #. If one side of the triangle has a length of #18 #, what is the largest possible area of the triangle?

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Answer 1 · 2017-12-11T07:39:25

Largest possible area of the triangle is 458.776

Given are the two angles #(5pi)/8# and #pi/12# and the length 18

The remaining angle:

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

I am assuming that length AB (18) is opposite the smallest angle.

Using the ASA

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

Area#=( 18^2*sin((7pi)/24)*sin((5pi)/8))/(2*sin(pi/12))#

Area#=458.776#