Two corners of a triangle have angles of (3 pi ) / 8 3π8 and pi / 3 π3. If one side of the triangle has a length of 6 6, what is the longest possible perimeter of the triangle?

1 Answer
sankarankalyanam
Dec 8, 2017

Largest possible area of the triangle is 18.1531

Explanation:

Given are the two angles (3pi)/83π8 and pi/3π3 and the length 6

The remaining angle:

= pi - (((3pi)/8) + pi/3) = (7pi)/24=π−((3π8)+π3)=7π24

I am assuming that length AB (1) is opposite the smallest angle.

Using the ASA

Area=(c^2*sin(A)*sin(B))/(2*sin(C)=c2⋅sin(A)⋅sin(B)2⋅sin(C)

Area=( 6^2*sin(pi/3)*sin((3pi)/8))/(2*sin((7pi)/24)=62⋅sin(π3)⋅sin(3π8)2⋅sin(7π24)

Area=18.1531=18.1531

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