Are they crazy?

Addalia is a big town near Jableh at western Syria, It's located near a mountain, and people who live in Addalia say that on a sunny clear day they can see the island of Cyprus from the top of the mountain. In this problem we're going to determine if they can really see Cyprus, and how high they need to be on the mountain to begin to see the coast of Cyprus.

Find \(h\), the viewing height (in m) required to see Cyprus from Addalia.

Details and assumptions:

  • Assume that the earth is completely spherical.
  • The straight line distance between Addalia and the Cyprus coastline 123.2km.
  • The Earth radius is 6400 km.
  • Addalia's mountain is 1083.5m high.
  • Note the height could be more than the height of the mountain, i.e. if \(h\leq1083.5\) m, the coast can't be seen.

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