A triangle has two corners with angles of # pi / 6 # and # (3 pi )/ 8 #. If one side of the triangle has a length of #4 #, what is the largest possible area of the triangle?

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Answer 1 · 2017-12-11T08:02:57

Largest possible area of the triangle is 14.6556

Given are the two angles #(3pi)/8# and #pi/6# and the length 1

The remaining angle:

#= pi - ((3pi)/8) + pi/6) = (11pi)/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#=( 4^2*sin((11pi)/24)*sin((3pi)/8))/(2*sin(pi/6))#

Area#=14.6556#