5. Summary

Converting between angles and directions isn't difficult, but there are a few things someone new to the computations needs to watch out for.

(1) Incorrect bearing quadrant.

This usually happens when the sketch isn't correctly drawn. In the diagram below, the surveyor assumed line JK was in the NE quadrant.

The bearing angle is the difference between the back bearing and the angle J. Based on his sketch, the surveyor recorded the bearing JK as S 8°19'15" E while it really is N 08°19'15" W. While a sketch helps, an incorrectly drawn one can lead to wrong answers.

(2) Bearing angle exceeds 90°

In this example, the surveyor computed the bearing angle as the sum of the back bearing angle and angle M, recording the bearing of line MN as N 91°05'45" E

When a bearing angle exceeds 90°,  the line crosses into the adjacent quadrant. Line MN's correctly written bearing  is S 88°54'15" E
 

(3) Using the East-West line

Directions are always referenced to a meridian, a North-South line. When performing calculations, angles should never be computed from the East-West line as it may lead to confusion. Students working with directions early on tend to break up angles into smaller parts, often computing parts from the East-West line. For example, in the following sketch, an intermediate calculation may be:

Bearing line RS is N 70°19'30" W from:

(4) Math mistakes

Most errors are angle addition or subtraction mistakes. Angles are a mixed unit system, deg-min-sec. They are also a mixed base susyem: minutes and seconds both max out at 60 while degrees are unlimited, Manual calculatoins errors are usually the result of either or both  factors. Calculators with built-in degree conversion or direct deg-min-sec manipulation capabilities help reduce the problem, providing the user knows how to use the calculator. Although they can help simplify and streamline calculations, the surveyor should stil be capable of manual angle calculations.