Section 4.3 states that with no intervening obstacles, the optical line of sight can be expressed as

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Section 4.3 states that with no intervening obstacles, the optical line of sight can be expressed as d = 3.571h, where d is the distance between an antenna and the horizon in kilometers and h is the antenna height in meters. Using a value for the Earth’s radius of 6370 km, derive this equation. Hint: Assume that the antenna is perpendicular to the Earth’s surface, and note that the line from the top of the antenna to the horizon forms a tangent to the Earth’s surface at the horizon. Draw a picture showing the antenna, the line of sight, and the Earth’s radius to help visualize the problem.

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