What is the maximum broadcasting from a radio tower 1800 feet tall( approximately 0.34 mile)? The radius of Earth is approximately 3960 miles, and you can assume the ground around the tower is nearly flat. Round your answer to the nearest 10 miles.
50 miles
Draw a diagram ,and it's clear that the distance d to the horizon from height h obeys:
d^2 + r^2 = (r+h)^2
That should help
To calculate the maximum broadcasting distance from a radio tower, we need to use the formula for the horizon distance. The horizon distance (d) can be computed using the following equation:
d = √(2Rh + h²)
where:
- d is the horizon distance.
- R is the radius of the Earth.
- h is the height of the radio tower.
Given that the radius of the Earth (R) is approximately 3960 miles and the height of the radio tower (h) is approximately 0.34 miles, we can substitute these values into the equation:
d = √(2 * 3960 * 0.34 + 0.34²)
d ≈ √(2689.92 + 0.1156)
d ≈ √2690.0356
d ≈ 51.9 miles
Therefore, the maximum broadcasting distance from the 1800-foot tall radio tower is approximately 52 miles. Rounded to the nearest 10 miles, the answer is 50 miles.