A triangle has two corners with angles of $\frac{3 π}{4}$ $(3 pi ) / 4$ and $\frac{π}{12}$ $( pi )/ 12$ . If one side of the triangle has a length of $2$ $2$ , what is the largest possible area of the triangle?

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Answer 1 · 2017-12-05T12:53:26

Largest possible area of the $Delta = color (purple)(2.7321)$

Given are the two angles $(3pi)/4, pi/12$ and the length 2

The remaining angle:

$pi - ((3pi)/4+ pi/12) = (pi)/6$

I am assuming that length AB (2) is opposite the smallest angle.

Using the ASA

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

Area $=( 2^2*sin((3pi)/4)*sin((pi)/6))/(2*sin(pi/12))$

Area $=2.7321$

A triangle has two corners with angles of (3 pi ) / 4 3π4 (3 pi ) / 4 and ( pi )/ 12 π12 ( pi )/ 12 . If one side of the triangle has a length of 2 22 , what is the largest possible area of the triangle?