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## Homework Statement

A box of mass X kg hangs motionless from two ropes, as shown in the diagram. The angle of rope 1 is specified amount of degrees. Choose the box as the system. The x-axis runs to the right, the y-axis runs up, and the z-axis is out of the page.

What is the magnitude of |F2|?

## Homework Equations

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The equation for finding the magnitude of the force is Force/cos(theta).

The equation for finding the force on the x-axis is |F

_{2}|sin(theta).

## The Attempt at a Solution

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I understand that the formula for |F

_{2}| is F

_{2y}/cos(theta), but I was wondering what the concept behind it would be? My book describes it as using "directional" cosines? It

Also, for F

_{2x}, I'm extremely confused as to why the F

_{2}needs to be multiplied by sin(theta), rather than cosine theta, other than it just giving you F

_{2y}. My book doesn't say anything about finding F

_{2x}, but is it related to taking the derivative of cosine?

It seems counter-intuitive to use cosine for the y-axis and sine for the x axis, but that's the process to get the same value as the correct answer?

Here's the free body diagram:

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