Departure of a Traverse Leg

Departure is the east-west partner of latitude, and with azimuths measured from north it takes the sine. Together the pair converts a field book of distances and directions into coordinate differences that can be added up, adjusted and plotted. Positive departures run east, negative run west, and the sign falls out of the sine automatically for azimuths past 180°.

The reason both components matter is that either one alone is ambiguous. A course with a departure of 125 ft on a 250 ft leg could be heading at azimuth 30° or at 150° — north-east or south-east — and only the latitude settles it. That is precisely why the arcsine brain here is flagged: it returns the northern branch and leaves the choice to you. A worked example: a 250 ft course at azimuth 30° has a departure of 250 sin 30° = 125 ft east and a latitude of 250 cos 30° = 216.5 ft north, and the two squared and added return the 250 ft you started with, which is the first arithmetic check a party chief runs.