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.