Geodetic triangulation

Definition

Triangulation is the following method of locating points. Let $A$ and $B$ be points with known positions, and let $c = \abs{AB}$ be the length of the baseline $AB$ . Let $C$ be a point not on the line $AB$ , and let $\alpha = \angle CAB$ and $\beta = \angle ABC$ be the measured angles. Then $C$ is determined, on a given side of $AB$ , by $\abs{AC} = \frac{c \sin\beta}{\sin(\alpha + \beta)}, \qquad \abs{BC} = \frac{c \sin\alpha}{\sin(\alpha + \beta)},$ together with the direction of $AC$ given by $\alpha$ . Geodetic triangulation repeats this step over a network of triangles, each new side serving as the baseline of the next triangle.

Remarks

Example: with $c = 1$ km and $\alpha = \beta = 60^\circ$ , one gets $\abs{AC} = \sin 60^\circ / \sin 120^\circ = 1$ km, as expected for an equilateral triangle. Non-example: locating $C$ by measuring $\abs{AC}$ and $\abs{BC}$ directly uses no angles; that is trilateration. The formulas come from the law of sines, since the angle at $C$ is $\pi - \alpha - \beta$ . Over large distances the triangles lie on the ellipsoid, and spherical or ellipsoidal corrections are applied. In practice more angles are measured than needed, and the network is adjusted by least squares.

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Angle at a point concept
Euclidean distance concept
Triangle concept
Law of sines statement
Geodetic triangulation definition

Tag	`BW9D1TN107`
URI	`m2://BW9D1TN107`
Kind	definition
Writing	W0 stub
MSC	86A30, 51N20
Defines	Geodetic triangulation
Uses	Law of sines
Changed	3 November 2026

Geodetic triangulation

Definition

Remarks

Reading path

Further reading

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