Finding an angle with Newton's Second Law

[Mr Davis 97]

Homework Statement

Given the free-body diagram below, and that the body is in equilibrium, find θ.

Homework Equations

F = ma

The Attempt at a Solution

[/B]
Basically, I used Newton's second law in the y direction.

Here is my work:

This does not seem like the correct answer, because the angle is acute. Thus, what am I doing wrong?

 

[SammyS]

Homework Statement

Given the free-body diagram below, and that the body is in equilibrium, find θ.
[ IMG]http://i.imgur.com/ee3VjBf.jpg[/PLAIN]

Homework Equations

F = ma

The Attempt at a Solution

[/B]
Basically, I used Newton's second law in the y direction.

Here is my work?
[ IMG]http://i.imgur.com/o4KjcyS.jpg[/PLAIN]
This does not seem like the correct answer, because the angle is acute. Thus, what am I doing wrong?

First of all, the three forces may have equal magnitude, but they are not equal as vectors.

That should be cos(θ/2) or equivalently sin(90° - θ/2)

 

[Mr Davis 97]

First of all, the three forces may have equal magnitude, but they are not equal as vectors.

That should be cos(θ/2) or equivalently sin(90° - θ/2)

So θ = 120 degrees?

 

[SammyS]

So θ = 120 degrees?

Yes.