Question

If the height of a TV transmitting antenna is 128 m, how much square area can be covered by the transmitted signal if the receiving antenna is at the ground level?

(Radius of the Earth = 6400 km)

Answer 1

Given: h = 128 m, R = 6400 km – 6400 × 10³ m

To find: Area covered (A)

Formulae: i. d = \(\sqrt{2Rh}\)

ii. A = πd²

Calculation:

From formula (i),

= 4.048 × 10⁴

= 40.48 km

From formula (ii).

Area covered = 3.142 × (40.48)²

= antilog [log 3.142 + 2log 40.48]

= antilog [0.4972 + 2(1.6073)]

= antilog [3.7118]

= 5.150 × 10³

= 5150 km²