Calculate the tension in leg A.

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Multiple Choice

Calculate the tension in leg A.

Explanation:
In this kind of rigging tension problem, static equilibrium governs everything: the forces at the connection must balance so there is no net force. Start with a free‑body diagram of the connection where the legs meet and the load is applied. You have the tensions in the legs and the external load acting downward. Resolve each leg’s tension into horizontal and vertical components using the angles given for each leg. Then set up two equilibrium equations: the sum of vertical components must equal the vertical load, and the sum of horizontal components must cancel to zero. In symbols, the vertical components add up to the load, and the horizontal components sum to zero. With the numbers from the diagram (the angles and the other tensions), you solve these two equations for the tension in leg A. The value that satisfies both equations is the tension in leg A; in this problem it comes out to 1607 units. This result makes sense: leg A’s angle determines how much vertical support its tension provides per unit of tension, so solving for T_A to balance the vertical load while keeping horizontal forces in balance determines the exact 1607 value.

In this kind of rigging tension problem, static equilibrium governs everything: the forces at the connection must balance so there is no net force. Start with a free‑body diagram of the connection where the legs meet and the load is applied. You have the tensions in the legs and the external load acting downward.

Resolve each leg’s tension into horizontal and vertical components using the angles given for each leg. Then set up two equilibrium equations: the sum of vertical components must equal the vertical load, and the sum of horizontal components must cancel to zero. In symbols, the vertical components add up to the load, and the horizontal components sum to zero. With the numbers from the diagram (the angles and the other tensions), you solve these two equations for the tension in leg A.

The value that satisfies both equations is the tension in leg A; in this problem it comes out to 1607 units. This result makes sense: leg A’s angle determines how much vertical support its tension provides per unit of tension, so solving for T_A to balance the vertical load while keeping horizontal forces in balance determines the exact 1607 value.

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