How is a back azimuth calculated if the azimuth is less than 180 degrees?

To calculate a back azimuth when the original azimuth is less than 180 degrees, the process involves subtracting 180 degrees from the initial azimuth. The reason for this is that azimuths are measured in degrees in a clockwise direction starting from true north (0 degrees).

When you have an azimuth of less than 180 degrees, it indicates a direction that is in the northeastern quadrant of the compass. To find the back azimuth, which represents the opposite direction, you need to consider that moving forward in one direction and then turning around (or going back) essentially means being on the opposite side of a circle. Subtraction effectively flips the angle to point in the opposite direction of travel. Thus, by subtracting 180 degrees from an azimuth of less than 180, you correctly derive the precise angle pointing in the opposite direction.

In contrast, if the original azimuth were greater than or equal to 180 degrees, you would instead need to add 180 degrees to find the back azimuth, as this would take you back around the circle to the opposite heading. This understanding highlights the importance of distinguishing between azimuths below and above 180 degrees when performing navigational calculations.