# Dictionary Definition

triangulation

### Noun

1 a trigonometric method of determining the
position of a fixed point from the angles to it from two fixed
points a known distance apart; useful in navigation

2 a method of surveying; the area is divided into
triangles and the length of one side and its angles with the other
two are measured, then the lengths of the other sides can be
calculated

# User Contributed Dictionary

## English

### Noun

- A technique in surveying in which distances and directions are estimated from an accurately measured baseline and the principles of trigonometry
- The network of triangles, so obtained, that are the basis of a map or chart
- In navigation or seismology, a process by which an unknown location is found using three known distances from known locations.
- A delaying move in which the king moves in a triangular path in order to force the advance of a pawn.
- Using multiple researchers to interview the same people or to evaluate the same evidence to reduce the impact of individual bias. [ref (1)] "Triangulation was established by asking researcher #2 and researcher #4 to conduct their own interview of the participant".

#### Related terms

References

(1) (Nahid Golafshani, 2003) Understanding
Reliability and Validity in Qualitative Research, The Qualitative
Report Volume 8 Number 4 December 2003 597-607, http://www.nova.edu/ssss/QR/QR8-4/golafshani.pdf

# 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

triangulation in Bulgarian: Триангулация

triangulation in Czech: Triangulace

triangulation in German: Triangulation
(Geodäsie)

triangulation in Spanish: Triangulación

triangulation in French: Triangulation

triangulation in Croatian: Triangulacija

triangulation in Indonesian: Triangulasi

triangulation in Italian: Triangolazione

triangulation in Hebrew: טריאנגולציה

triangulation in Hungarian: Háromszögelés

triangulation in Dutch: Driehoeksmeting

triangulation in Norwegian: Triangulering

triangulation in Polish: Triangulacja
(geodezja)

triangulation in Russian: Триангуляция

triangulation in Slovenian: Triangulacija

triangulation in Swedish:
Triangulering

# Synonyms, Antonyms and Related Words

appraisal, appraisement, approximation, assessment, assize, assizement, automatic
tracking, calculation, computation, correction, data
transmission, determination, estimate, estimation, evaluation, flector tuning,
gauging, instrumentation, locking
on, locking signals, mapping, measure, measurement, measuring, mensuration, metric system,
phase adjustment, pinpointing, precision
focusing, quantification, quantization, radar
navigation, radar-telephone relay, range finding, rating, scan conversion, scanning, signal modulation,
survey, surveying, telemetering, telemetry, three-pointing,
tracking, triggering
signals, valuation