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Why do surveyors measure at least one baseline in a triangulation system?

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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).

In surveying and civil engineering, a triangulation system relies on the laws of plane trigonometry, which dictate that if one side and two angles of a triangle are known, the remaining sides and angles can be calculated.1

Surveyors measure at least one baseline—a side of a triangle—with great care to serve as the foundational length for the entire system. By establishing this known distance, all other side lengths in the network can be derived trigonometrically from the measured angles.213

Measuring a baseline is essential for several reasons:
* Framework Calculation: It provides the necessary scale for the entire triangulation network, allowing for the computation of distances that might otherwise be difficult or impossible to measure directly.1
* Geometric Consistency: In complex systems like quadrangles, measuring a baseline and all angles allows surveyors to verify the accuracy of the network by ensuring that computations through different sets of adjacent triangles yield consistent results.4
* Verification: Measuring a second baseline in a large system provides a critical check on the work, as the calculated length should closely agree with the actual measured length.3