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Triangulation principle; third-order specifications

Short answer

Triangulation starts with a measured baseline; angles from its ends to a third station determine the other sides by the sine rule, extending across a network. Third‑order triangulation: sides 1.5–10 km, baseline 0.5–3 km, average triangle closure 6″, maximum 12″, base error 1 in 250 000.

Explain the principle of triangulation. List out the general specification of third order triangulation survey.

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) is then 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 specification of third order (tertiary) triangulation

ItemSpecification
Length of base line0.5 to 3 km
Length of sides of triangles1.5 to 10 km
Average triangular error (closure)6"
Maximum triangular error12"
Probable error of base line1 in 250,000
Discrepancy between two measures of the base20 mm K\sqrt{K} (KK in km)
Probable error of computed distance1 in 5,000 to 1 in 20,000

✓ Answer checked by Claude Opus 5.5 (high effort)

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