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).

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

triangulation observations.

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