Question

A tv transmission tower antenna is at a height of 20 m. How much range can it cover if the receiving antenna is at a height of 25 m?

Answer 1

A tv transmission tower antenna is at a height

H(t) = 20 m

receiving antenna is at a height

H(r) = 25 m

And

R = 6.4 × 10^6

Where R is a radius of earth curvature

Distance between transmitter and receiver ( line of sight)

D = √2RH(t) + √2RH(r)

D = √{2×6.4×(10)^6 × 20} + √{2×6.4×(10)^6 ×25 }

D = √{128 × (10)^5 × 20} + √{128 × (10)^5 × 25 }

D = 16000 + 17888.543

D = 33888.543 meter

D = 33888.543 × 1/(10)^3

D = 33.888 KM

Area covered

A = πD^2

A = ( 22/7 ) × ( 33.888 )^2

A = 22/7 × 1148.396

A = 3609.246 square KiloMeters

range area covered

Answer- 3609.246 square KiloMeters