So long radio song

Ever flown on and airplane and seen the blinking lights on top of a radio tower? It may seem odd to build towers tall enough to cause trouble for airplanes, but there's a reason radio towers are tall. The taller the tower, the larger the range over which people can get the signal as FM radio waves are roughly limited by line of sight to the tower. This is why there can be lots of FM stations on the same frequency - they have a limited geographic region. To get an idea of the size of the region, consider a tower on top of a mountain such that the total height of the tower above sea level is 2 km. How far away can you be from the base of the tower/mountain (X in the picture) in kilometers before you lose line of sight to it? Remember - the earth is curved...

Details and assumptions

  • The radius of the earth is 6370 km.
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