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How does trigonometric leveling determine the elevation of an inaccessible point?
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surveying
Figure 1: Photogrammetric photographs from two short, overlapping flight strips arranged for supplying mapping details. Photo-control points are shown on only one photograph; shading indicates a typical terrain feature such as a lake (see text).
Trigonometric leveling is a method used in surveying to determine the elevation of points, particularly when they are inaccessible or when standard spirit leveling is impractical.12
To determine the elevation of an unknown point using this technique, the following steps are typically taken:
- Establish Horizontal Position: The horizontal position of the inaccessible point is first determined using triangulation from two or more points of known position and elevation.1
- Measure Vertical Angles: A theodolite is used to measure the vertical angles from the known stations toward the target point.12
- Compute Elevation: Using the known horizontal distances and the measured vertical angles, the difference in elevation between the known points and the unknown point is calculated through trigonometric functions.1
This method is faster than spirit leveling and is especially useful in hilly terrain where many points are located on hilltops. To improve precision, observations are often made simultaneously in both directions to help eliminate errors caused by aerial refraction.2