$\"\"$

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

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Magnitudes of the force vectors $\"\"$ equals to 1000 pounds.

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Write each force vector in terms of the unit vectors $\"\"$ and j.

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$\"\"$ .

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$\"\"$ .

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$\"\"$ .

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For static equilibrium the sum of the force vectors is equal to zero.

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$\"\"$

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$\"\"$

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$\"\"$

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From (1),

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$\"\"$

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Substitute $\"\"$ in (2)

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ pounds.

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$\"\"$

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The two tension forces are $\"\"$ pounds and $\"\"$ pounds.