Two corners of a triangle have angles of $(5 pi )/ 12$ and $pi / 6$ . If one side of the triangle has a length of 12, what is the longest possible perimeter of the triangle?

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Answer 1 · 2017-12-08T14:05:32

Largest possible area of the triangle is 134.3538

Given are the two angles $(5pi)/12$ and $pi/6$ and the length 12

The remaining angle:

$= pi - (((5pi)/12) + pi/6) = (5pi)/12$

I am assuming that length AB (12) is opposite the smallest angle.

Using the ASA

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

Area $=( 12^2*sin((5pi)/12)*sin((5pi)/12))/(2*sin(pi/6))$

Area $=134.3538$

Two corners of a triangle have angles of (5 pi )/ 12 (5 pi )/ 12 and pi / 6 pi / 6 . If one side of the triangle has a length of 12, what is the longest possible perimeter of the triangle?