Two corners of a triangle have angles of #(3 pi ) / 4 # and # pi / 6 #. If one side of the triangle has a length of #5 #, what is the longest possible perimeter of the triangle?

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Answer 1 · 2017-12-08T13:50:01

Largest possible area of the triangle is 17.0753

Given are the two angles #(3pi)/4# and #pi/6# and the length 5

The remaining angle:

#= pi - (((3pi)/4) + pi/6) = pi/12#

I am assuming that length AB (5) is opposite the smallest angle.

Using the ASA

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

Area#=( 5^2*sin(pi/6)*sin((3pi)/4))/(2*sin(pi/12))#

Area#=17.0753#