Final Answer:
The 4th shower that overlaps with the primary spheres is positioned at an angle of 60 degrees from the central axis.
Step-by-step explanation:
In the given scenario, we are dealing with the placement of the 4th shower concerning the primary spheres. To determine its position accurately, we consider the geometry of spheres and the concept of angles. In a spherical arrangement, each sphere contributes 90 degrees to the total angle around the central axis. As there are three primary spheres, they collectively cover 270 degrees (3 * 90 degrees).
To find the position of the 4th shower, we subtract this sum from a complete circle (360 degrees). Therefore, 360 - 270 equals 90 degrees. However, since the question specifies an overlap, we divide this angle by 2 to distribute it evenly between the adjacent spheres. The result is 45 degrees. Adding this to the angle covered by each sphere (90 degrees), we find that the 4th shower is positioned at an angle of 135 degrees from the starting point. Considering the circular symmetry, we further divide this by 2 to find the final position about the central axis, resulting in an angle of 60 degrees.
In conclusion, the 4th shower overlaps with the primary spheres at an angle of 60 degrees from the central axis, providing a comprehensive understanding of its placement in the spherical arrangement.