# 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

- to locate by means of triangulation
- 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.

- Victor
Davis Hanson,

# 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):

- The sum of the angles of a triangle is π radians or 180 degrees.
- The law of sines
- The law of cosines
- The Pythagorean theorem

## 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

- GSM localization
- Multilateration, where a point is calculated using the time-difference-of-arrival between other known points
- Parallax
- Real-time locating
- Resection
- SOCET SET
- Stereopsis
- Trig point
- Trilateration, where a point is calculated given its distances from other known points

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

allocate, appraise, appreciate, assay, assess, assign, calculate, calibrate, caliper, check a parameter,
collocate, compute, deploy, dial, dispose, divide, emplace, estimate, evaluate, fathom, fix, gauge, get a fix, graduate, home in on, install, localize, locate, measure, mensurate, mete, meter, navigate, pace, pin down, pinpoint, place, plumb, position, prize, probe, put in place, quantify, quantize, rate, situate, size, size up, sound, span, spot, step, survey, take a reading, valuate, value, weigh, zero in on