There are several methods used in angular measurements as discussed in this paper. Albeit the standard magnetic compass has been used to give approximate values of angles, it has several inherent problems such as the inability to correctly align with the earth's rotational axis. As a result, more efficient devices like the transits or theodolites have been developed to rectify the error in magnetic compasses. The theodolite comprises a telescope for spotting distant objects, bubble levels for ensuring that the angles are accurate, and two measurement wheels for determining the vertical and horizontal angles. Transits are less complicated than the theodolite although the components are fundamentally similar.
Another method of angular measurement is by using total station which comprises electronic distance and angular measuring techniques of the theodolite in a single unit. For measuring the intersection lines of sight, Gannett (2016, p.46) notes that the vertical and horizontal positions can be determined based on the control networks. In that regard, the position of a point about two axes gives the horizontal location. They are the prime meridian and the equator lines which are also equivalent to the x and y coordinates on a Cartesian plane.
Measurements in a surveying operation are typically done in positional series. Beginning from control points, the surveyors utilise the trigonometric ratios to determine the locations of positions within the Cartesian axes. The errors that arise from the operation are quantified by adding up the sum of the interior angles obtained from the polygon formed on the plane. Since it is not possible to know the accuracy of just a single angle, the traverse can be evaluated in its entirety to distribute the errors across all the interior angles (Gannett 2016, p.56).
Triangulation is also a method of angular measurement. It involves the use of a more equipped theodolite to measure the horizontal sight distances electronically. As the name suggests, triangulation measures the three inner angles of a triangle and the length of one of the side. After that, trigonometric rules are employed to determine the dimensions of the remaining distances.
A corollary to triangulation is trilateration. The procedure determines the positions of points by using distances alone. It is relatively more straightforward to perform since it is inexpensive and uses fewer tools. It eschews the angle measurements and employs the trigonometric principle to determine the dimensions of the distances (Gannett 2016, p.56).
Reference
Gannett, H. (2016). Manual Of Topographic Methods (Classic Reprint). [S.L.]: Forgotten Books.
