A back azimuth is a projection of the azimuth from the origin to the opposite side of the azimuth circle. There are 360 degrees in the azimuth circle, so the opposite direction would be 180 degrees (half of 360 degrees) from the azimuth.
A back azimuth is calculated by adding 180° to the azimuth when the azimuth is less than 180°, or by subtracting 180° from the azimuth if it is more than 180°. For example, if an azimuth is 320°, the back azimuth would be 320° - 180° = 140°. If the azimuth is 30°, the back azimuth would be 180° + 30° = 210°.
Backsighting is a method of sighting that uses an azimuth reading taken backwards. Backsighting uses the azimuth sight and turns it around to find the way back to the original starting point.
Example 1 - Susan is at the lookout point and sights a fire at 100°. She starts out in the direction of the fire, but soon loses sight of the fire. Susan turns around and backsights to the lookout point. It is 260°. How many degrees off course is she? Which direction does Susan need to move to get back on course?
Step 1. The azimuth, 260°, is more than 180°, so subtract 180° from the azimuth. 260° 180°= 80°
Step 2. Subtract the calculated backsight reading from the original azimuth reading.
100° - 80° = 20°
Susan is 20 degrees off course.
Because the new azimuth (80°) is less than the original (100°), Susan needs to move to the left to make the back azimuth larger by 20°. When the lookout line of sight back azimuth of 280° is read, she can proceed along the line toward the fire.
Susan needs to move to the left by 20 degrees.