Question 4

Explanation

Problem Visualization

Here is an illustration of the spotlight positions (at the top corners) and the intersection point of their beams.

Geometric Analysis

The spotlights are installed at the four top corners of the room (points $E$, $F$, $G$, $H$ in the figure). The beams meet at one point. Since the room is cube-shaped and the light positions are symmetrical, this intersection point must be exactly in the center of the cube (the intersection of the space diagonals).

The distance from the center of the cube to the floor (plane $ABCD$) is half of the cube's height (edge length).

Given the edge length $s = 5$ meters.

Then the distance from the intersection point to the floor is:

So, the distance from the intersection point to the floor is $2\frac{1}{2}$ meters.