$\"\"$

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The static equilibrium weight of $\"\"$ is suspended from two cables.

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The tensions in the cables are the magnitudes $\"\"$ and $\"\"$ of the force vectors $\"\"$ and $\"\"$ .

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The magnitude of the force vector $\"\"$ equals $\"\"$ , the weight of the box.

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Now write each force vector in terms of the unit vectors $\"\"$ and $\"\"$ . $\"\"$ is the angle between the vector and the positive $\"\"$ -axis.

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Draw the related diagram:

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$\"\"$

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Observe the diagram:

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$\"\"$ .

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$\"\"$ .

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$\"\"$ .

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Substitute $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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The tensions in the two cables are $\"\"$ and $\"\"$ .

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$\"\"$

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The tensions in the two cables are $\"\"$ and $\"\"$ .