QJEEM23Phe872: JEE Main 2023 Physics - Class 12 JEEM23Phe872 Solution: The height of transmitting antenna is and the height of the…

$$d_{max}=\sqrt{2R{h}_t}+\sqrt{2R{h}_r}$$

where $d_{\max}$ is the maximum distance between the antennas, $R$ is the radius of the earth, $h_t$ is the height of the transmitting antenna above the earth's surface, and $h_r$ is the height of the receiving antenna above the earth's surface.

Substituting the given values, we get:

$$d_{max}=\sqrt{2\times 6400\mathrm{km}\times 180\mathrm{m}}+\sqrt{2\times 6400\mathrm{km}\times 245\mathrm{m}}=104\mathrm{km}$$

Therefore, the maximum distance between the transmitting and receiving antennas for line of sight communication is $\boxed{104\,\mathrm{km}}$ .