Final answer:
The exact timeframe for reporting a death involving hoisting equipment is not stated, but the Triangle Shirtwaist Fire underscores the importance of timely reporting and stringent safety regulations.
Step-by-step explanation:
The specific timeframe for when the department of Public Safety must be notified of a death involving hoisting equipment is not detailed within the scenario provided. Such regulations are generally set by Occupational Safety and Health Administration (OSHA) or analogous local safety departments. However, referencing the Triangle Shirtwaist Fire tragedy highlights the importance of workplace safety measures and the need for prompt reporting and rigorous safety protocols. The tragedy led to public support for stricter building codes and regulations, which would presumably include timely incident reporting.