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Triangulation versus trilateration
Short answer
Triangulation measures a single base line and all angles, then computes sides by the sine rule; it is time‑consuming and needs clear visibility. Trilateration measures all sides directly with an EDM instrument and computes angles by the cosine rule; it is faster, works in poor visibility with microwave, but requires costly instruments and atmospheric corrections.
Differentiate between triangulation and trilateration (with advantages and disadvantages).
Triangulation is a method of horizontal control survey in which control stations are fixed at the vertices of a chain or net of triangles. One side (the base line) is measured very accurately, all the angles of the triangles are measured, and the lengths of the other sides are computed with the sine rule.
Trilateration is the method in which the lengths of all the sides of the triangles are measured directly with an EDM (electromagnetic distance measuring) instrument, and the angles are computed from the sides using the cosine rule.
Differences
| Basis | Triangulation | Trilateration |
|---|---|---|
| Measured quantities | One base line and all angles | All sides of all triangles |
| Instrument | Theodolite (precise) | EDM / total station |
| Computed quantities | Other sides (sine rule) | Angles (cosine rule) |
| Control | Check base line at the end | Closure of the figure; no separate base |
| Weather | Needs good visibility for signals; angles affected by refraction | Atmospheric conditions (temperature, pressure) affect the measured distance; works in poor visibility with microwave EDM |
| Field work | Time-consuming; many angles observed in sets | Fast; each side measured in minutes |
| Accuracy | Depends on angle measurement; errors accumulate with distance | Distances very accurate with modern EDM; better control of scale |
| Orientation | Azimuth must be observed | Azimuth must be observed separately (no angles) |
| Cost | Higher fieldwork cost | Lower fieldwork cost today |
Advantages of triangulation: needs only one base line; theodolite angle measurement is reliable; suitable for large areas; well-established practice.
Disadvantages of triangulation: base line measurement is laborious; angular observation is slow and needs signals/towers; errors accumulate.
Advantages of trilateration: quick, with no angle measurement or base-line extension; EDM gives high accuracy; works in low visibility (microwave); needs fewer observers.
Disadvantages of trilateration: needs costly EDM; atmospheric corrections are necessary; fewer checks on gross errors unless the figure has redundant sides; gives no azimuth.
✓ Answer checked by Claude Opus 5.5 (high effort)
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