A triangle has two corners with angles of # pi / 6 # and # (5 pi )/ 8 #. If one side of the triangle has a length of #2 #, what is the largest possible area of the triangle?

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Answer 1 · 2017-12-08T12:18:46

Largest possible area of the triangle is 2.2497

Given are the two angles #(7pi)/12# and #pi/4# and the length 2

The remaining angle:

#= pi - (((5pi)/8) + pi/6) = (5pi)/24#

I am assuming that length AB (2) is opposite the smallest angle.

Using the ASA

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

Area#=( 2^2*sin((5pi)/24)*sin((5pi)/8))/(2*sin(pi/6))#

Area#=2.2497#