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Triangulation

From Biocrawler, the free encyclopedia.

This article is about measurement by the use of triangles: for other usages of the term "triangulation", see triangulation (disambiguation).

The ship wants to know the distance d to the shore. The ship measures angles α and β, and knows length l, so it can apply the law of sines to find the distance.

In trigonometry and elementary geometry, triangulation is the process of finding a distance to a point by calculating the length of one side of a triangle, given measurements of angles and sides of the triangle formed by that point and two other reference points.

Some identities often used (valid only in flat or euclidean geometry):

The sum of the angles of a triangle is π (180 degrees).
The law of sines
The law of cosines
The Pythagorean theorem

Triangulation is used for many purposes, including surveying, navigation, astrometry, binocular vision and gun direction of weapons.

Many of these surveying problems involve the solution of large meshes of triangles, with hundreds or even thousands of observations. Complex triangulation problems involving real-world observations with errors require the solution of large systems of simultaneous equations to generate solutions.

Famous uses of triangulation have included the retriangulation of Great Britain.

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