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What Is the Angle of Elevation?

Trigonometry can be used to solve for unknown values.
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  • Written By: C.B. Fox
  • Edited By: Susan Barwick
  • Last Modified Date: 08 October 2014
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The angle of elevation is the measure of the angle formed by the horizontal plane in which an observer is located and an object above the horizontal plane. The observer stands at the vertex of the angle. The intersection of the rays of the angle with the vertical line from the object to the horizontal plane form a right triangle. There are a number of ways to determine this angle, given a known height and distance, and devices such as sextants can be used to measure the angle. Given a known angle of elevation, it is possible to determine the height and distance of the observed object.

If the observer is directly below the object whose angle of elevation is being measured, the angle is 90 degrees. An object on the same horizontal plane as the observer has an elevation of zero degrees. The measure of the angle of elevation can fall anywhere between these two values.

Though the sextant is the tool traditionally used to measure the angle of elevation of celestial objects for navigational purposes, it can be used to determine the angle of elevation of any object. To use a sextant, the observer holds the tool up to one eye and points it towards the elevated object. Degree markings on the sextant indicate the angle formed by the horizontal plane of the observer and the intersecting ray that points toward the elevated object.

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The geometrical and mathematical concepts associated with right triangles can be used to determine unknown values of distance and angle, and simple trigonometry can be used to solve for unknown values as long as at least two are known. If the height of the object and the distance between the observer are known, the angle of elevation can be determined by finding the tangent of the angle — the ratio of height to distance. If the angle and either height or distance are known, the unknown can be determined in the same fashion. It is also possible to determine the angle of elevation when given only one known value, though this requires the use of more advanced trigonometric concepts.

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