Q. A TV transmission tower has a height of 140 m and the height of the receiving antenna is 40 m. What is the maximum distance upto which signals can be broadcasted from this tower in LOS(Line of Sight) mode ? (Given : radius of earth = $6.4 \times 10^6m$).

Solution:

Maximum distance upto which signal can be broadcasted is
$d_{max } = \sqrt{2Rh_{T}} + \sqrt{2Rh_{R}} $
where $h_T$ and $h_R$ are heights of transmiter tower and height of receiver respectively.
Putting all values -
$d_{max } = \sqrt{2 \times6.4 \times106} \left[\sqrt{104} + \sqrt{40}\right] $
on solving, $d_{max } $ = 65 km

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