Two corners of a triangle have angles of #(3 pi ) / 8 # and # pi / 4 #. If one side of the triangle has a length of #9 #, what is the longest possible perimeter of the triangle?

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Answer 1 · 2017-12-08T15:22:04

Largest possible area of the triangle is 48.8878

Given are the two angles #(3pi)/8# and #pi/4# and the length 9

The remaining angle:

#= pi - (((3pi)/8) + pi/4) = (3pi)/8#

I am assuming that length AB (9) is opposite the smallest angle.

Using the ASA

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

Area#=( 9^2*sin((3pi)/8)*sin((3pi)/8))/(2*sin(pi/4))#

Area#=48.8878#