length or side is known, and all three angles are measured. The other lengths or sides of the triangles are
computed by applying the law of sines (sin) (Figure 2-1).
Figure 2-1. Solving Angles and Using the Law of Sines
b. To begin work on a net of triangulation, the length of the starting line is required. The final
computation of the positions of the new stations, as well as the final azimuths, is done after the
triangulation is complete from one line of known length to another and after the net has been adjusted.
The azimuth, latitude, and longitude are obtained from astronomic observations made during or after the
2-34. Classification of Triangulation. The basis of classification of triangulation is the accuracy with
which the length and azimuth of a line of the triangulation are determined. Higher order triangulation is
performed under two primary orders of accuracy. These orders are subdivided to give a total of five
different degrees of precision. The principal criterion is that the discrepancy between the measured
length of a baseline and its length, as computed through the triangulation net from the next preceding
base, shall not, after adjustment, be greater than the length closure shown for each class.
a. First-Order Triangulation. There are three classes of first-order triangulation.
Class I surveys are the most precise class of survey and must have a length closure of 1 part
in 100,000. Its use is generally restricted to surveys for scientific purpose. These include
establishing and testing missile and satellite systems, and performing studies of the shifting
of the earth's crust and the tilting of landmasses. Class I is also the basis for accurate land
surveys in highly developed areas.
Class II must have a length closure of 1 part in 50,000. The basic national-control net should
be composed of arcs of triangulation of this