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12.3: Azimuth and Elevation

Difficulty Level: At Grade Created by: CK-12


An old surveyor's telescope (theodolite).

The surveyor's telescope is designed to measure two such angles. The angle  \phi is measured counterclockwise in a horizontal plane, but surveyors (and soldiers) work with azimuth, a similar angle measured clockwise from north. Thus the directions (north, east, south, west) have azimuth (0°, 90°, 180°, 270°). A rotating table allows the telescope to be pointed in any azimuth.

The angle  \lambda is called elevation and is the angle by which the telescope is lifted above the horizontal (if it looks down,  \lambda is negative). The two angles together can in principle specify any direction:  \phi ranges from 0 to 360, and  \lambda from –90 (straight down or “nadir") to +90 (straight up or “zenith").

Again, one needs to decide from what direction is the azimuth measured--that is, where is azimuth zero? The rotation of the heavens (and the fact most humanity lives north of the equator) suggests (for surveyor-type measurements) the northward direction, and this is indeed the usual zero point. The azimuth angle (viewed from the north) is measured counterclockwise.

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Date Created:

Feb 27, 2012

Last Modified:

Jan 21, 2015
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