A triangle has two corners with angles of # pi / 4 # and # 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 · 2017-12-11T08:06:59

Largest possible area of the triangle is 3.4142

Given are the two angles #(pi)/8# and #pi/4# and the length 2

The remaining angle:

#= pi - ((pi)/8) + pi/4) = (5pi)/8#

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((5pi)/8)*sin((pi)/4))/(2*sin(pi/8))#

Area#=3.4142#