A triangle has two corners with angles of # (3 pi ) / 4 # and # ( pi )/ 6 #. If one side of the triangle has a length of #4 #, what is the largest possible area of the triangle?

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Answer 1 · 2017-12-20T11:39:46

Largest possible area of the triangle #Delta = 10.9282#

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

The remaining angle:

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

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((3pi)/4)*sin((pi)/6))/(2*sin(pi/12))#

Area#=10.9282#