A triangle has two corners with angles of # pi / 2 # and # (3 pi )/ 8 #. If one side of the triangle has a length of #9 #, what is the largest possible area of the triangle?

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Answer 1 · 2017-12-08T14:17:05

Largest possible area of the triangle is 97.7756

Given are the two angles #(pi)/2# and #(3pi)/8# and the length 9

The remaining angle:

#= pi - ((pi)/2) + (3pi)/8) = (pi)/8#

I am assuming that length AB (9) is opposite the smallest angle.

Using the ASA

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

Area#=( 9^2*sin(pi/2)*sin((3pi)/8))/(2*sin(pi/8))#

Area#=97.7756#