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Principle of triangulation and trilateration

Short answer

In triangulation, a baseline is measured; all angles of the triangle network are observed, and remaining sides are computed using the sine law, with a check baseline at the end. Trilateration measures all sides of each triangle with EDM, then computes angles via the cosine law, eliminating the need for angle observations or baseline extension.

Write a short note on the principle of triangulation and 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) 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

Principle of trilateration

If the three sides a, b, c of a triangle ABC are measured, any angle is found with the cosine rule:

cos⁡A=b2+c2−a22bc\cos A = \frac{b^2 + c^2 - a^2}{2bc}

The sides are measured by EDM, so no angles are observed and no base line extension is needed. The figure is solved from the lengths alone.

✓ Answer checked by Claude Opus 5.5 (high effort)

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