Acable holds a weight of 100 pounds, what is the tension at 30 degrees

The tension in the cable when it is at angle of 30° to the vertical is 86.6 lb.

refer to the attached diagram.

The cable has a weight W attached to it and it is at an angle θ 30° to the vertical.

Resolve the weight W into two components W cos θ opposite to the tension T and W sinθ perpendicular to it, as shown in the diagram.

Apply the condition for equilibrium along the direction in which the tension acts.

Substitute 100 lbs for W and 30° for θ.

Thus the tension in the cable when it is at an angle 30° to the vertical is 86.6 lb.

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