A triangle has two corners with angles of $(2 pi ) / 3$ and $( pi )/ 6$ . If one side of the triangle has a length of $6$ , what is the largest possible area of the triangle?

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Answer 1 · 2017-12-08T13:26:44

Largest possible area of the triangle is 15.5885

Given are the two angles $(2pi)/3$ and $pi/6$ and the length 6

The remaining angle:

$= pi - (((2pi)/3) + pi/6) = pi/6$

I am assuming that length AB (6) is opposite the smallest angle.

Using the ASA

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

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

Area $=15.5885$

A triangle has two corners with angles of (2 pi ) / 3 (2 pi ) / 3 and ( pi )/ 6 ( pi )/ 6 . If one side of the triangle has a length of 6 6 , what is the largest possible area of the triangle?