A triangle has two corners with angles of $(3 pi ) / 4$ and $( pi )/ 6$ . If one side of the triangle has a length of $3$ , what is the largest possible area of the triangle?

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Answer 1 · 2017-12-08T15:11:11

Largest possible area of the triangle is 6.1471

Given are the two angles $(3pi)/4$ and $pi/6$ and the length 3

The remaining angle:

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

I am assuming that length AB (3) is opposite the smallest angle.

Using the ASA

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

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

Area $=6.1471$

A triangle has two corners with angles of (3 pi ) / 4 (3 pi ) / 4 and ( pi )/ 6 ( pi )/ 6 . If one side of the triangle has a length of 3 3 , what is the largest possible area of the triangle?