G. Horizontal Angles

1. Definition

A horizontal angle is measured perpendicular to gravity. Three points are involved:

  • Backsight (BS)

  • Foresight; FS

  • At


The angle is between two vertical planes; one contains the BS and At points, the other contains the FS and At. The At point is generally occupied by a surveying instrument, Figure G-1.


Figure G-1
Horizontal Angle

If we look down on the horizontal plane with the three points, Figure G-2, we see there are two horizontal angles between the vertical planes: HAng1 and HAng2.


Figure G-2
Two Horizontal Angles

This causes an ambiguous situation unless we can specifically identify which angle we mean. Recall that the four parts of an angle are:

  • Start

  • Direction

  • Magnitude

  • End


HAng1 and HAng2 have the same start (BS) and end (FS) but different direction and magnitude. All four parts must be clearly defined. Merely including magnitude without a direction doesn’t resolve the ambiguity. For example, a 135° angle from BS to FS could still be interpreted two ways, Figure G-3.



Figure G-3
Magnitude without Direction

Similarly, expressing a direction, to the right (clockwise) or left (counterclockwise), without a magnitude is also unclear, Figure G-4.


Figure G-4
Direction without Magnitude

There are a few different ways to specify horizontal angles which help minimize confusing interpretations.