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Triangulation principle; 1st order trilateration

Short answer

A baseline is measured and angles at its ends to a third point are observed; sides are computed by the sine rule, extending the network. First‑order trilateration: all sides measured with EDM, sides 30–150 km (microwave) or shorter with infrared, accuracy 1 part in 100 000 or better, well‑conditioned triangles, meteorological corrections applied, and closure checked.

Explain the principle of triangulation. List out the general specifications of 1st order trilateration.

Principle of triangulation

The base line AB is measured accurately. At A and B the angles to a third station C are measured. In triangle ABC, the sides AC and BC are computed by the sine rule:

ABsin⁡C=BCsin⁡A=ACsin⁡B\frac{AB}{\sin C} = \frac{BC}{\sin A} = \frac{AC}{\sin B}

The computed side BC (or AC) then becomes the base for the next triangle BCD, and so on. The whole area is covered by a chain or net of triangles. At the end, a second base line (check base) is measured and compared with its computed length; the difference shows the accuracy of the work. Azimuth is observed at the ends to control the direction.

      C-----E-----G
     / \   / \   / \
    /   \ /   \ /   \
   A-----B-----D-----F
   base                   check base

General specifications of first order trilateration

ItemFirst order trilateration (usual specification)
MethodAll sides measured by EDM (infrared or microwave)
Length of sidesAbout 30 - 150 km for primary control with long-range (microwave) EDM; infrared EDM reaches only a few km (up to about 10 to 15 km), so sides are shorter
Accuracy of distance1 part in 100,000 or better (for example ±(5 mm+1 ppm)\pm (5\ \text{mm} + 1\ \text{ppm}))
FigureWell-conditioned triangles; all angles between 30 and 120 degrees; braced quadrilaterals or polygons with central points
ObservationsEach side measured in both directions and in at least two sets; temperature, pressure and humidity recorded
CorrectionsMeteorological, instrument constants, slope and reduction to mean sea level
CheckClosure of the figure and comparison of computed and measured sides

(The first order values follow common geodetic standards; they may be revised by the Survey Department.)

If the paper means first order triangulation: base line 5 to 15 km, sides 30 to 150 km, average triangular error less than 1", maximum triangular error 3", probable error of base 1 in 1,000,000, and probable error of computed distances 1 in 60,000 to 1 in 250,000.

✓ Answer checked by Claude Opus 5.5 (high effort)

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