Triangulation and Trilateration
Survey2 Notes of AM Fillone, DLSU-Manila
Triangulation and trilateration are employed extensively to
establish horizontal control for topographic mapping; charting
lakes rivers, and ocean coast lines; and for public surveys required
for the design and construction of public and private works of
large extent
A triangulation system consist of a series of joined or
overlapping triangles in which an occasional line is measured and
the balance of the sides are calculated from angles measured at
the vertices of the triangles. The lines of a triangulation system
form a networks that ties together all the triangulation stations at
the vertices of the triangles.
A trilateration system also consists of a series of joined or
overlapping triangles. However, for trilateration all of the lengths
of the triangle sides are measured and the few directions or
angle observed are only those required to establish azimuth.
Survey2 Notes of AM Fillone, DLSU-Manila
The work of triangulation consists of the following steps:
1. Reconnaissance to select the location of stations.
2. Preanalysis through error propagation to evaluate the
geometric strength of the proposed network.
3. Setting station marks, erecting signals, and setting towers for
elevating signals or instruments where needed.
4. Observations of directions or angles.
5. Measurement of base lines.
6. Astronomic observations at one or more stations to determine
the true meridian to which azimuths are referred.
7. Computations, including reduction to the ellipsoid, calculation
of all lengths of triangle sides and coordinates for all triangulation
stations, and adjustment of the triangulation network to provide
the best estimates of coordinates for all points.
Source: Surveying Theory and Practice, 7th Ed., by Anderson and Mikhail, p. 305.
Survey2 Notes of AM Fillone, DLSU-Manila
Triangulation Figures. A triangulation or trilateration system may consist of:
Survey2 Notes of AM Fillone, DLSU-Manila
Survey2 Notes of AM Fillone, DLSU-Manila
Survey2 Notes of AM Fillone, DLSU-Manila
Important Formulas in Trigonometry
Sine Law:
b

c
a
Cosine Law:
Survey2 Notes of AM Fillone, DLSU-Manila


Other Important Trigonometric Identities
Sin (x + y) = sin x cos y + cos x sin y
Sin (x – y) = sin x cos y – cos x sin y
Cos (x + y) = cos x cos y – sin x sin y
Cos (x – y) = cos x cos y + sin x sin y
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Example:
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Solution:
Survey2 Notes of AM Fillone, DLSU-Manila
Survey2 Notes of AM Fillone, DLSU-Manila
EXAMPLE
It was also known that <ACB and <BDE are right triangles and line AC is parallel to
BD. Determine the lengths of all lines of the triangulation system.
Survey2 Notes of AM Fillone, DLSU-Manila
Survey2 Notes of AM Fillone, DLSU-Manila
Survey2 Notes of AM Fillone, DLSU-Manila
Seatwork No. 4 (20 pts) – use ½ sheet of paper
Survey2 Notes of AM Fillone, DLSU-Manila