A transmitting antenna at the top of a tower has a height 32m and...

Given,

Height of transmitting antenna is, ${h}_{T} = 50m$

Height of receiving antenna is, ${h}_{R} = 32m$

Thus, maximum distance for satisfactory communication will be,

${d}_{M} = \sqrt{2R{h}_{T}} + \sqrt{2R{h}_{R}}$ where $R$ is radius of the Earth,

${d}_{M} = \sqrt{2R{h}_{T}} + \sqrt{2R{h}_{R}}{d}_{M} = \sqrt{2 \times 64 \times {10}^{5} \times 50} + \sqrt{2 \times 64 \times {10}^{5} \times 32}{d}_{M} = 8000\sqrt{10} + 6400\sqrt{10}{d}_{M} = 14400\sqrt{10}m{d}_{M} = 45536 . 7m{d}_{M} = 45 . 5km$