When using a two-leg sling with both legs at angle θ from vertical, what is the tension in each leg?

• A. T = W / (2 sin θ)
• B. T = W cos θ
• C. T = W / 2
• D. T = W / (2 cos θ)

Answer: (D)

When lifting a weight with a two-leg sling that forms the same angle with the vertical on each leg, the load is held up by the vertical components of the two tensions. Because the setup is symmetric, the tensions in both legs are equal. The vertical component of each leg’s tension is T cos θ, and these two vertical components must add up to the weight W. So 2 times T cos θ equals W.

Solving for T gives T = W / (2 cos θ). This matches the expected behavior: as θ increases (legs more spread out), cos θ decreases and the required tension grows; when θ is zero (legs vertical), T equals W/2, meaning each leg carries half the load.

It would be incorrect to use sin here since sin would relate to the horizontal component; the vertical support comes from the cos component because the angle is measured from the vertical.