A 6-foot tall man wishes to buy a plane mirror in which he can visualize his whole length at the same time. How tall must the mirror measure in order for the above to occur?

To determine the height of a mirror necessary for a 6-foot tall man to see his entire reflection, it's essential to understand how reflection works in a plane mirror. When a person looks into a mirror, they can see their entire body if the mirror is at least half their height. This is because the line of sight from the eyes to the bottom of the feet and back to the mirror forms two right triangles, where the reflection occurs at the midpoint.

For a 6-foot tall individual, half of that height is 3 feet. Therefore, a 3-foot tall mirror will suffice to allow the man to see his whole length. This is based on the geometric principles of reflection, where the height needed for reflection is influenced by the angle at which light travels. Consequently, a mirror that is 3 feet in height will allow him to fully view his entire body from head to toe.