Q.Is it necessary for a transmitting antenna to be at the same height as that of the receiving antenna for line-of-sight communication? A TV transmitting antenna is 81 m tall. How much service area can it cover if the receiving antenna is at the ground level?

Is equal height necessary? No. The maximum line-of-sight range is $d_M=\sqrt{2Rh_T}+\sqrt{2Rh_R}$ — a sum of two independent terms, one for each antenna's own height. The two heights can be different; the formula still applies (if $h_R=0$, that term simply vanishes).

Given: transmitting antenna height $h_T = 81$ m, receiving antenna at ground level so $h_R = 0$, $R = 6.4\times10^{6}$ m.

Step 1 — Range (radius of coverage).

With $h_R=0$:

Step 2 — Service area. …

Since $d_M=\sqrt{2Rh_T}+\sqrt{2Rh_R}$ sums two independent terms, unequal heights are fine. With the receiver at ground level, only the transmitter term survives: $d=\s …

• Assuming LOS communication requires the transmitting and receiving antennas to be the same height.
• Forgetting to square the range when computing the service area (using $\pi d$ instead of $\pi d^2$). …