triangulation
A technique in which distances and directions are estimated from an accurately measured baseline and the principles of trigonometry; (countable) an instance of the use of this technique.
triangulation: using angles to measure distance and location
Triangulation is a surveying method that establishes position and distance by measuring angles from a known baseline. A surveyor measures the length of one baseline precisely, then observes the angles to a distant point from each end of that baseline. Using trigonometry, the two angles and the baseline length determine both the distance to that point and its exact location. This avoids the need to measure long distances directly across rough ground, water, or obstacles.
The method requires at least two observation stations and a target point. The baseline should be as long as practical, often ranging from tens of metres for local surveys to kilometres for regional work. The angles are measured using a transit, theodolite, or total station. Once the angles are recorded, simple trigonometry solves for the unknown distances. When multiple triangles share common sides and angles, the network extends across large areas, building up a framework of points whose positions are all mathematically locked to the original baseline measurement.
Small-scale triangulation might use a single triangle to locate a building corner or boundary point from two known reference marks. Large-scale triangulation, historically called triangulation networks or chains, covered entire countries. The first-order triangulation of Great Britain, completed over decades in the 18th and 19th centuries, used baselines several miles long and connected thousands of points with measuring angles to arc seconds of accuracy. Modern surveying often replaces long triangulation chains with GPS and GNSS methods, but triangulation remains essential where electronic positioning is unavailable, unreliable, or where tie-in to older surveys is needed.
Triangulation's accuracy depends on the baseline measurement, the angle measurements, and the length of the triangle sides. Angles measured to one arc minute can introduce positional errors of roughly one part in 3,500; professional surveys often demand arc-second precision or better. Long thin triangles, where the target point lies nearly along the baseline extension, give poor results because small angle errors produce large distance errors. Well-shaped triangles, close to equilateral, minimize error propagation.
The term reflects the method itself: three points define any triangle, and solving one triangle from two angles and a side is pure trigonometry. When surveyors chain multiple triangles across landscape, the term applies to the entire systematic network as well as to each individual calculation. Triangulation remains common in mine surveys, tunnelling, large structural monitoring, and boundary establishment, wherever angle measurement is more practical or precise than linear distance measurement.