# A transmitting antenna at the top of a tower has a height 32 m and the height of the receiving antenna is 50 m. What is the maximum distance between them for satisfactory communication in line of sight (LOS) mode ? Option 1) 55.4 km     Option 2)  45.5 km Option 3)  54.5 km   Option 4) 455 km

P Plabita

As we have learnt,

Range of transmitting antenna -

$d_{T}= \sqrt{2h_{T}R}$

- wherein

$h_{T}=$ height of antenna

$R=$ Radius of earth

Range $= \sqrt{2Rh_r} + \sqrt{2Rh_R}$

$\\= \sqrt{2\times6400\times 10^3\times 32} + \sqrt{2\times 6400\times 10^3\times 50}\\ = \sqrt{64\times 64 \times 10^5} + \sqrt{64\times 10^7}\\=6400\sqrt{10} + 8000\sqrt{10} m\\=14400\sqrt{10} = 45.5 km$

Option 1)

55.4 km

Option 2)

45.5 km

Option 3)

54.5 km

Option 4)

455 km

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