A transmitting antenna is at a height of 40 m and the receiving antenna is at a height of 60 m. The maximum distance between them for satisfactory communication is nearly

Given,

$$\begin{gathered} H_T=40 \\ {H}_R=60 \end{gathered}$$

The radius of the area that the television broadcast is intended to cover is directly proportional to the height of the transmitting antenna, a fundamental component of radio technology:

$$\begin{gathered} d_{max}=\sqrt{2R{H}_T} \\ \Rightarrow d_{max}=\sqrt{2R{H}_T}+\sqrt{2R{H}_R} \\ \Rightarrow d_{max}=\sqrt{\frac{2\times 6400\times 40}{1000}}+\sqrt{\frac{2\times 6400\times 60}{1000}} \\ \Rightarrow d_{max}=8\sqrt{8}+8\sqrt{12} \\ \Rightarrow d_{max}=50km \end{gathered}$$

Hence the correct answer is 50km.