Two corners of a triangle have angles of # (3 pi )/ 8 # and # ( pi ) / 2 #. If one side of the triangle has a length of # 12 #, what is the longest possible perimeter of the triangle?

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Answer 1 · 2017-12-08T12:58:16

Largest possible area of the triangle is 347.6467

Given are the two angles #(3pi)/8# and #pi/2# and the length 12

The remaining angle:

#= pi - (((3pi)/8) + pi/2) = pi/8#

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#=( 12^2*sin(pi/2)*sin((3pi)/8))/(2*sin(pi/8))#

Area#=347.6467#