Final answer:
The maximum radio communication distance between two 2 km high towers, considering the Earth's radius of about 6,000 km and assuming direct line of sight, is 310 km.
Step-by-step explanation:
When two radio transmission towers of equal height are involved, the maximum radio range or communication distance can be estimated using geometric principles. The radios must have a line of sight to each other, which means the signal needs to clear the curvature of the Earth. We can calculate the range using the formula for the distance to the horizon from an observer above the surface: ∑ = √(2 * height * radius of Earth) for each tower and then sum the distances for both. Here, the radius of the Earth (R) is roughly 6,000 km, and the height of the towers (h) is 2 km for each.
For one tower, the horizon distance is ∑ = √(2 * 2 km * 6,000 km) = √(24,000 km²) = 155 km. For two towers, you would double this distance, giving you 310 km as the maximum communication distance using straight-line radio waves between two 2 km high towers. This does not take into account any atmospheric effects or obstacles that might further limit the range.