A triangle has two corners with angles of # (2 pi ) / 3 # and # ( pi )/ 4 #. If one side of the triangle has a length of #12 #, what is the largest possible area of the triangle?

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Answer 1 · 2017-12-08T09:53:16

Largest possible area of the triangle = 4.7321

Given are the two angles #(2pi)/3# or #120^@# and #pi/4# or #45^@# and the length 12

The remaining angle:

#180^@-(120^@+45^@)=15^@#

I am assuming that length AB (12) is opposite the smallest angle.

Using the ASA

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

Area#=( 2^2*sin(45)*sin(120))/(2*sin(15))#

Area#=4.7321#