Article Index

1. Base line

Intersections are used to compute the coordinates of an unknown point from two known points, Figure D-1. Determining a position requires a combination of triangle solutions along with inverse and forward computations.

img41
Figure D-1
Unknow Point Related to Base line

 

Two points with known coordinates (A and B) form one side of a triangle; inversing between them gives the length and direction of that side (the base line).

Two other measurements must be made from the base line in order to compute the remaining parts of the triangle and solve point C's position. The measurements can consist of two angles, two distances, or an angle and a distance. Why two measurements? Because at point C there are two unknowns: NC & EC. To solve them we need two measurements linked to known positions. 

With those measurements you then have the required three triangle parts including a length. After the remaining parts of the triangle are solved, the coordinates of the unknown point (C) can be computed using a forward computation.

It is important to remember that in the following discussions there are just enough measurements made to solve for the unknown location: two measurements to solve two unknowns. An error in one or more measurement will not be apparent in the computations unless the error results in an impossible geometry condition. The surveyor should always include additional measurements in order to provide an independent check.