At what distance will a RADAR beam be more than 57 feet wide?

The width of a RADAR beam increases with distance. Generally, the beam width can be approximated using the formula which relates beam width and distance, showing that as you move further away from the source, the beam spreads out and the effective width increases.

At a significant distance, such as 300 feet, the divergence of the beam will lead to a width that exceeds 57 feet. This spreading occurs because of the physical properties of radars, which emit a cone-shaped beam that widens as it travels further from the source.

The other distances, such as 150 feet, 200 feet, and 250 feet, fall short of causing the beam to exceed the 57-foot width, illustrating how the beam width is still constrained at these shorter ranges. Therefore, only at 300 feet does the RADAR beam cross the threshold into a width greater than 57 feet, making it the correct answer.