Two corners of a triangle have angles of (5 pi )/ 8 5π8 and ( pi ) / 6 π6. If one side of the triangle has a length of 7 7, what is the longest possible perimeter of the triangle?

1 Answer
sankarankalyanam
Dec 8, 2017

Largest possible area of the triangle is 27.5587

Explanation:

Given are the two angles (5pi)/85π8 and pi/6π6 and the length 7

The remaining angle:

= pi - (((5pi)/8) + pi/6) = (5pi)/24=π−((5π8)+π6)=5π24

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=( 7^2*sin((5pi)/24)*sin((5pi)/8))/(2*sin(pi/6))=72⋅sin(5π24)⋅sin(5π8)2⋅sin(π6)

Area=27.5587=27.5587

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