7.1 Bearings, Azimuths, and Direction Conversions

Bearings, Azimuths, and Direction Conversions

The FS exam includes Survey Computations and Computer Applications as an official knowledge area, and direction handling is one of the fastest ways to lose or gain time. A bearing, azimuth, deflection angle, and included angle can all describe direction, but they are not interchangeable until you convert them to the same reference. The practical exam habit is to convert every line to an azimuth first, normalize it, and then compute latitude and departure from that azimuth.

An azimuth is measured clockwise from north. North is 0 deg or 360 deg, east is 90 deg, south is 180 deg, and west is 270 deg. A quadrant bearing uses an acute angle and a quadrant label. For example, N 35 deg E is in the northeast quadrant and converts to azimuth 35 deg. S 35 deg E is in the southeast quadrant and converts to 145 deg. S 35 deg W converts to 215 deg, and N 35 deg W converts to 325 deg.

Back direction is another common trap. If the forward azimuth is less than 180 deg, add 180 deg. If it is 180 deg or more, subtract 180 deg. Then normalize the result so it stays in the 0 to 360 deg range. A line with azimuth 47 deg has back azimuth 227 deg. A line with azimuth 284 deg has back azimuth 104 deg.

Traverse questions may give a starting bearing and a series of deflection or interior angles. A right deflection angle is added to the previous azimuth. A left deflection angle is subtracted. For interior angles in a closed polygon, draw the turn or use a consistent traverse orientation. If you guess clockwise versus counterclockwise without a sketch, a correct arithmetic process can still point the line into the wrong quadrant.

The FS setting is computer-based, and NCEES provides electronic reference material during the exam. That does not remove the need to know which direction convention you are using. Handbook formulas can only help after the line direction is correct. Practice converting degrees, minutes, and seconds before entering trig values. For example, 28 deg 15 min 30 sec equals 28 + 15/60 + 30/3600 = 28.258333 deg.

Use a short direction checklist:

1. Identify whether the given direction is an azimuth, quadrant bearing, deflection, or angle from another line.
2. Convert the direction to decimal degrees if minutes and seconds are present.
3. Convert quadrant bearings to azimuths using the quadrant rule.
4. Apply right or left deflections with the correct sign.
5. Normalize any result below 0 deg or at least 360 deg.
6. Before computing coordinates, check that the quadrant matches the expected field sketch.

A realistic problem might state that a boundary line runs S 72 deg 20 min E for 426.50 ft. The azimuth is 107 deg 40 min because southeast bearings use 180 deg minus theta. The line should have negative latitude and positive departure. If your computed coordinate change is northing positive, the trigonometry or sign convention is wrong even if the calculator accepts the number.