Propagation of electromagnetic waves

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Question

A transmitting antenna at the top of a tower has a height of 45 m and the receiving antenna is on the ground. If the maximum distance between them for satisfactory communication in Line Of Sight mode ( $R = 6.4 \times 10^{6} m$ ) is $y \times 10^{3} m$ then y is

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Solution

$d = \sqrt{2 R h_{T}} + \sqrt{2 R h_{R}} P u t h_{T} = 45 m, h_{R} = 0, R = 6.4 \times 10^{6} m \Rightarrow d = \sqrt{2 \times 6.4 \times 10^{6} \times 45} + \sqrt{2 \times 6.4 \times 10^{6} \times 0} \Rightarrow d = 24 \times 10^{3} m$

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