The question relates to visual acuity and the distance at which a tag's signal word must be legible; however, without explicit safety guidelines or context, a specific numerical answer cannot be provided. It's advised to refer to relevant workplace safety standards for accurate requirements.
The student's question hints at the need to determine the maximum distance at which a tag's signal word must be readable, which is related to visual acuity and the concept of legibility distance. According to the information provided, the smallest letters on the Snellen chart that a person with normal vision should be able to read subtend 5 minutes of an arc from 20 feet away. From this, we can derive that a tag's signal word must be designed to be legible at a distance where it subtends an appropriate angle for its intended level of visibility.
In the case of the person who can read the 75.0 cm high letters with a visual acuity that forms an image 4.00 µm high on their retina, we can calculate the maximum distance using similar triangles. However, a specific numeric distance threshold for a tag's readability is not provided in the references. Presumably, the required distance for tag signal word readability would depend on the context in which the tag is used and the standards set by any overseeing safety or regulatory bodies.
So, the question seems to revolve around occupational safety or signage standards, but without a specific standard or context provided, a numerical answer can't be given. It's advisable to consult workplace safety guidelines or the specific standard referenced in the course material to determine the minimum distance requirement.