SOLUTION: The maximum distance that a radio signal can reach directly is the length of the segment tangent to the curve of the Earth's surface. If the angles formed by the tangent radio sign

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Question 591382: The maximum distance that a radio signal can reach directly is the length of the segment tangent to the curve of the Earth's surface. If the angles formed by the tangent radio signals and the tower are 89.5 degrees, what is the measure of the intercepted arc of the Earth? Given that the radius of Earth is approximately 4000 miles, estimate how far the signal can reach.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The maximum distance that a radio signal can reach directly is the length of the segment tangent to the curve of the Earth's surface.
If the angles formed by the tangent radio signals and the tower are 89.5 degrees, what is the measure of the intercepted arc of the Earth?
Given that the radius of Earth is approximately 4000 miles, estimate how far the signal can reach.
:
We can solve this as a right triangle using the tangent of 89.5
let d = side representing the distance from the tower to the horizen
tan(89.5) = 4000%2Fd
114.58865 = 4000%2Fd
d = 4000%2F114.58865
d = 34.907 miles
:
The difference between the arc of the earth and the distance from the tower to the horizon is negligible