Q.A transmitting antenna at the top of a tower has a height 32 m and the height of the receiving antenna is 50 m. What is the maximum distance between them for satisfactory communication in LOS mode? Given radius of earth $6.4 \times 10^{6}$ m.

Given: height of transmitting antenna $h_T = 32$ m, height of receiving antenna $h_R = 50$ m, radius of Earth $R = 6.4\times10^{6}$ m.

Step 1 — Range formula.

For line-of-sight (space wave) propagation, the transmitting antenna "sees" the horizon at a distance $d_T=\sqrt{2Rh_T}$, and the receiving antenna at height $h_R$ can be reached from a point up to $d_R=\sqrt{2Rh_R}$ beyond that horizon. So the maximum distance between the antennas for satisfactory communication is

Step 2 — Compute $d_T$.

Step 3 — Compute $d_R$.

Step 4 — Add.

Line-of-sight range is the sum of each antenna's individual horizon distance: $d_M=\sqrt{2Rh_T}+\sqrt{2Rh_R}$. Substitute $R=6.4\times10^{6}$ m and the two antenna heights, then add the two square-root terms — do not average or use a single combined-height formula.

• Using $d=\sqrt{2Rh}$ with only one antenna's height (forgetting the receiving antenna also contributes a horizon distance).
• Mixing up radius and diameter of Earth, or forgetting to convert km to m before substituting.
• Adding the heights ($h_T+h_R$) before taking the square root instead of adding the two separate square-root terms.