A triangle has two corners with angles of # pi / 12 # and # (7 pi )/ 8 #. If one side of the triangle has a length of #6 #, what is the largest possible area of the triangle?

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Answer 1 · 2017-12-05T12:27:00

Largest possible area of the triangle = 8.0031

Given are the two angles #(7pi)/8# or #157.5^@# and #pi/12# or #15^@# and the length 6

The remaining angle:

#180^@-(157.5^@+15^@)=17.5^@#

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#=( 6^2*sin(17.5)*sin(157.5))/(2*sin(15))#

Area#=8.0031#