A triangle has two corners with angles of # ( pi ) / 2 # and # ( 5 pi )/ 12 #. If one side of the triangle has a length of #1 #, what is the largest possible area of the triangle?

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Answer 1 · 2017-12-11T05:20:21

Largest possible area of the triangle is 1.866

Given are the two angles #(pi)/2# and #5pi/12# and the length 1

The remaining angle:

#= pi - ((pi)/2) + (5pi/12) = (pi)/12#

I am assuming that length AB (1) is opposite the smallest angle.

Using the ASA

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

Area#=( 1^2*sin(pi/2)*sin((5pi)/12))/(2*sin(pi/12))#

Area#=1.866#