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When working on a ladder, wearing slip-resistant footwear is crucial because it significantly enhances traction and stability on the ladder's rungs. Slip-resistant shoes help prevent slips and falls, which are common hazards associated with ladder use. They provide a secure grip, helping workers maintain their balance and reducing the risk of accidents.

While other safety equipment, such as hard hats or safety goggles, may be beneficial in various situations to protect against different hazards, they do not specifically contribute to maintaining stability when ascending or descending a ladder. Gloves may also help in providing a better grip, but they do not address the risk of slipping in the same manner as appropriate footwear. Therefore, slip-resistant footwear is essential for ensuring safety while working on a ladder, making it the most relevant choice in this context.