The height of a T.V tower is 100m . If radius of earth is 6400km, then what is the maximum distance of transmission from it.
Answers
Answer:
Maximum distance of transmission = 35.78 km
Step by step explaination:
Height of the tower H = 100 m = 0.1 km
Redius of earth R = 6400 km
To find the Maximum distance of transition, we need to dra a tangen to the earth surface from the top of the tower. (See the figure).
Thus, from point B, when tangent drawn, it will touch the earch at point C.
BC will be the maximum distance of tansmission.
As point C is at tangent, ∠C = 90°
AC = Redius of earth = 6400 km
AB = Redius of earth + Height of tower
∴AB = 6400 + 0.1 km = 6400.1 km
To find BC; using Pythagoras Theorem
AB² = AC² + BC²
∴ BC² = AB² - AC²
∴ BC² = 6400.1² - 6400²
∴ BC² = (6400.1+6400)×(6400.1-6400)
∴ BC² = 12800.1 × 0.1
∴ BC² = 1280.01
∴ BC = 35.78 km
Maximum distance of transmission = 35.78 km
