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Distance to Horizon

Grade:
6-8, 9-12
Standards:
AlgebraGeometry
Math Content:
Algebra, Geometry

Because of the curvature of the Earth, it is possible to see to some point in the distance (what we call the horizon). The horizon is actually the point of tangency formed by the tangent line from your eye to the surface of the Earth. As your height above the Earth increases, the farther away the horizon appears.

This applet allows you to explore the relationship between your height above the Earth and the distance you can see to the horizon.

Sorry, this page requires a Java-compatible web browser.
Change the height above sea level by dragging the point labeled Height. The height will be displayed. Note that the height is given in feet.

Based on the height, the distance to the horizon will be automatically calculated. Note that the distance to the horizon is given in miles. Also note that the image is not drawn to scale.

The peak of Mount Everest, the tallest mountain on Earth, occurs 29,035 feet above sea level. (The mountain shown in the applet represents Mount Everest.) If you were standing at the summit of Everest, how many miles would you be able to see to the horizon?

Most of us will never get to the top of Mount Everest. But it might be interesting to know how far you can see to the horizon from other heights. How many miles could you see to the horizon from…

  • the crow's nest of a pirate ship?
  • the window of a jet airplane?
  • the top of Taipei 101, a 101-story building in Taipei, Taiwan, whose top is 1671 feet above sea level? What if you were at the top of other tall buildings like the Sears Tower, the Petronas Towers, or the Empire State Building?
  • the highest point in your state?

Can you find a rule that will allow you to predict the distance d to the horizon (in miles), if you know your height h (in feet) above sea level?