The heights of two antennas above the earth are `h_T` and `h_R` respectively. The maximum line of sight distance` d_M `between the two antennas is (R→Radius of earth)

Options

A. `d_m=sqrt2Rh_T-sqrt2Rh_R`
B. `d_m=(sqrt2Rh_T-sqrt2Rh_R)^2`
C. `d_m=sqrt2Rh_T+sqrt2Rh_R`
D. `d_m=(sqrt2Rh_T+sqrt2Rh_R)^2`

Answer

To find the maximum line of sight distance \( d_M \) between two antennas situated at heights \( h_T \) and \( h_R \) above the Earth's surface, we can use the following steps:

### Step-by-Step Solution:

1. **Understanding the Geometry**:
- The maximum line of sight distance from an antenna to the horizon can be derived from the geometry of a circle (the Earth) and a tangent line (the line of sight).
- For an antenna at height \( h \), the distance to the horizon \( d \) can be approximated using the formula:
\[ d = \sqrt{2Rh} \]
where \( R \) is the radius of the Earth.

2. **Calculate Distance for Each Antenna**:
- For the transmitting antenna at height \( h_T \):
\[ d_T = \sqrt{2Rh_T} \]
- For the receiving antenna at height \( h_R \):
\[ d_R = \sqrt{2Rh_R} \]

3. **Total Maximum Line of Sight Distance**:
- The total maximum line of sight distance \( d_M \) between the two antennas is the sum of the distances to the horizon from each antenna:
\[ d_M = d_T + d_R = \sqrt{2Rh_T} + \sqrt{2Rh_R} \]

4. **Final Expression**:
- Thus, the maximum line of sight distance \( d_M \) can be expressed as:
\[ d_M = \sqrt{2R} \left( \sqrt{h_T} + \sqrt{h_R} \right) \]

### Conclusion:
The maximum line of sight distance \( d_M \) between the two antennas at heights \( h_T \) and \( h_R \) above the Earth is given by:
\[ d_M = \sqrt{2R} \left( \sqrt{h_T} + \sqrt{h_R} \right) \]