1. Triangulation and Trilateration
Survey2 Notes of AM Fillone, DLSU-Manila

2. 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

3. 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

4. Survey2 Notes of AM Fillone, DLSU-Manila
Triangulation Figures. A triangulation or trilateration system may consist of:
Survey2 Notes of AM Fillone, DLSU-Manila

5. Survey2 Notes of AM Fillone, DLSU-Manila

6. Survey2 Notes of AM Fillone, DLSU-Manila

7. 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

8. 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
Survey2 Notes of AM Fillone, DLSU-Manila

9. Survey2 Notes of AM Fillone, DLSU-Manila
Example:
Survey2 Notes of AM Fillone, DLSU-Manila

10. Survey2 Notes of AM Fillone, DLSU-Manila
Solution:
Survey2 Notes of AM Fillone, DLSU-Manila

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12. 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

13. Survey2 Notes of AM Fillone, DLSU-Manila

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15. Survey2 Notes of AM Fillone, DLSU-Manila
Seatwork No. 4 (20 pts) – use ½ sheet of paper
Survey2 Notes of AM Fillone, DLSU-Manila