# 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 $\times$ 106 m.

The maximum line-of-sight distance $d_M$ between two antennas having heights $h_T$ and $h_R$ above the earth is given by $d_M = \sqrt {2Rh_T} + \sqrt {2Rh_R}$ where $h_T$ and $h_R$ are the heights of the transmitting and receiving antennae.
Substituing, we get: $d_M = \sqrt { 2 \times 64 \times 10^5 \times 32} + \sqrt {2 \ times 64 \times 10^5 \times 50}\;m$
$d_M \;= 64 \times 10^2 \sqrt{10} + 8 \times 10^3 \times \sqrt{10}\;m$
$\quad \;\; =144 \times 10^2 \times \sqrt {10} \;m= 45.5\; km$