A triangle has two corners with angles of # (3 pi ) / 4 # and # ( pi )/ 8 #. If one side of the triangle has a length of #7 #, what is the largest possible area of the triangle?

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Answer 1 · 2017-12-08T10:01:21

Largest possible area = 17.3241

Given are the two angles #(3pi)/4# and #pi/8# and the length 7

The remaining angle:

#= pi - (((3pi)/4) + pi/8) = pi/8#

I am assuming that length AB (6) is opposite the smallest angle.

Using the ASA

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

Area#=( 7^2*sin(pi/8)*sin((3pi)/4))/(2*sin(pi/8))#

Area#=17.3241#