Two corners of a triangle have angles of # (5 pi )/ 8 # and # ( pi ) / 4 #. If one side of the triangle has a length of # 4 #, what is the longest possible perimeter of the triangle?

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Answer 1 · 2017-12-08T13:33:28

Largest possible area of the triangle is 13.6569

Given are the two angles #(5pi)/8# and #pi/4# and the length 4

The remaining angle:

#= pi - (((5pi)/8) + pi/4) = pi/8#

I am assuming that length AB (4) is opposite the smallest angle.

Using the ASA

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

Area#=( 4^2*sin(pi/4)*sin((5pi)/8))/(2*sin(pi/8))#

Area#=13.6569#