Math in Engineering

Civil Engineeringand Mathematics

How do surveyors make measurements?

Most of a surveyor’s measurements are gathered with a theodolite, an instrument that acts as a telescope, ruler, and protractor. The theodolite is set up over a known spot, such as a previously surveyed corner of a lot; its telescope then sights a specific spot, such as another corner of a lot, and the distance is measured (most modern theodolites use lasers to measure distance), supplemented by angular measurements in both the horizontal and vertical planes. The surveyor then uses trigonometry to analyze the data, converting it to a more usable form, usually in x, y, and z coordinates. For example, depending on the desired outcome, the vertical angle and slope distances can be converted from polar measurements to show differences in elevations and horizontal distances. The horizontal distances and angles can also be converted from polar measurements to rectangular coordinates. (For more about coordinates, see “Geometry and Trigonometry.”)


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