Two corners of a triangle have angles of $( pi )/ 3$ and $( pi ) / 4$ . If one side of the triangle has a length of $1$ , what is the longest possible perimeter of the triangle?

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Answer 1 · 2017-12-08T15:07:34

Largest possible area of the triangle is 0.7888

Given are the two angles $(pi)/3$ and $pi/4$ and the length 1

The remaining angle:

$= pi - ((pi)/4) + pi/3) = (5pi)/12$

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

Using the ASA

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

Area $=( 1^2*sin(pi/3)*sin((5pi)/12))/(2*sin(pi/4))$

Area $=0.7888$

Two corners of a triangle have angles of ( pi )/ 3 ( pi )/ 3 and ( pi ) / 4 ( pi ) / 4 . If one side of the triangle has a length of 1 1 , what is the longest possible perimeter of the triangle?