AskDefine | Define triangulate

Dictionary Definition

triangulate adj : composed of or marked with triangles

Verb

1 divide into triangles or give a triangular form to; "triangulate the piece of cardboard"
2 measure by using trigonometry; "triangulate the angle"
3 survey by triangulation; "The land surveyor worked by triangulating the plot"

User Contributed Dictionary

English

Verb

  1. to locate by means of triangulation
  2. to pit two others against each other in order to achieve a desired outcome or to gain an advantage; to "play both ends against the middle"
    • Victor Davis Hanson,
      It is one thing to triangulate between the United States and the Arab world for short-term advantage; quite another to find oneself alienated from the heretofore supportive Americans without finding commensurate gratitude from the Middle East.

Extensive Definition

In trigonometry and geometry, triangulation is the process of finding coordinates and 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 known reference points, using the law of sines.
In the figure at right, the third angle of the triangle (call it θ) is known to be 180 − α − β, since the sum of the three angles in any triangle is known to be 180 degrees. The opposite-side for this (the third) angle is l, which is a known distance. Since, by the law of sines, the ratio sin(θ)/l is equal to that same ratio for the other two angles α and β, the lengths of any of the remaining two sides can be computed by algebra. Given either of these lengths, sine and cosine can be used to calculate the offsets in both the north/south and east/west axes from the corresponding observation point to the unknown point, thereby giving its final coordinates.
Some identities often used (valid only in flat or euclidean geometry):

Calculation

  • α, β and distance AB are already known
  • C can be calculated by using the distance RC or MC:
  • RC: Position of C can be calculated using the Law of Sines
\gamma=180^\circ-\alpha-\beta
\frac=\frac=\frac
Now we can calculate AC and BC
AC=\frac
BC=\frac
Last step is to calculate RC via
RC=AC \cdot \sin\alpha
or
RC=BC \cdot \sin\beta
  • MC can be calculated using the Law of Cosines and the Pythagorean theorem
MR=AM-RB=\left(\frac\right)-\left(BC \cdot \cos\beta\right)
MC=\sqrt
Triangulation is used for many purposes, including surveying, navigation, metrology, astrometry, binocular vision, model rocketry 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.

See also

triangulate in Bulgarian: Триангулация
triangulate in Czech: Triangulace
triangulate in German: Triangulation (Geodäsie)
triangulate in Spanish: Triangulación
triangulate in French: Triangulation
triangulate in Croatian: Triangulacija
triangulate in Indonesian: Triangulasi
triangulate in Italian: Triangolazione
triangulate in Hebrew: טריאנגולציה
triangulate in Hungarian: Háromszögelés
triangulate in Dutch: Driehoeksmeting
triangulate in Norwegian: Triangulering
triangulate in Polish: Triangulacja (geodezja)
triangulate in Russian: Триангуляция
triangulate in Slovenian: Triangulacija
triangulate in Swedish: Triangulering

Synonyms, Antonyms and Related Words

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