Question

A transmitting antenna at the top of a tower has a height of $50\text{m}$ and the height of the receiving antenna is $80\text{m}$. What is the range of communication for Line of Sight (LoS) mode?
[Use radius of earth $=6400\text{km}$]

• A. $45.5\text{km}$
• B. $144.1\text{km}$
• C. $57.28\text{km}$
• D. $80.2\text{km}$

Answer 1

The correct option is C $57.28\text{km}$

Given :-
$R=6400\text{km}$
$H_t=50\text{m}$
$H_r=80\text{m}$

Range of communication is given by :
$R=\sqrt{2R{H}_t}+\sqrt{2R{H}_r}$
$R=\sqrt{2\times 6400\times 50\times {10}^{-3}}+\sqrt{2\times 6400\times 80\times {10}^{-3}}$
$R=8\sqrt{10}+32$
$\Rightarrow R=57.28\text{km}$