For a line running due east and west the departure would equal the length of the line and the latitude would be zero. Now, for a line running other than north to south or east to west, you can determine the latitude or departure by simple triangle solution. The latitude of a traverse line, then, equals the product of the length of the line times the cosine of the angle of bearing. To determine the departure, you solve the triangle for the length of the side CB shown in figure 7-10. Latitude equals length of traverse line times twine of angle of bearing.
Departure equals length of traverse line times sine of angle of bearing.
The departure of a traverse line, then, equals the length of the line times the sine of the angle of bearing. The latitude of a traverse line is designated north or south and the departure is designated east or west following the compass direction of the bearing of the line. A line bearing northeast, for example, has a north latitude and east departure. Graphic solution of a closed traverse by latitude and departure. In practice, as you will learn, the sum of the north latitudes usually differs from the sum of the south latitudes.