Two corners of a triangle have angles of # (5 pi )/ 8 # and # ( pi ) / 12 #. 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 · 2017-12-05T12:47:18

Largest possible area of the #Delta = color (purple)(27.1629)#

Given are the two angles #(5pi)/8, pi/12# and the length 5

The remaining angle:

#pi - ((5pi)/8+ pi/12) = (7pi)/24#

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((7pi)/24)*sin((5pi)/8))/(2*sin(pi/12))#

Area#=27.1629#