chapter  2
Pages 65

Departures and latitudes are X and Y components of a survey line superimposed onto a horizontal plane with a directional reference system. Mathematically, they are the legs of a right triangle, the hypotenuse being the line itself. This line can be considered as the resultant of two vectors, the vectors being the departure and latitude. In surveying, the X component (departure) lies in the east-west direction and the Y component (latitude) in the north-south direction. The departure can be abbreviated ∆X, meaning "difference in X coordinates" and the latitude can be called ∆Y, meaning "difference in Y coordinates." When distances and directions of a line are known, ∆X = L sin Z and ∆Y = L cos Z, the length being denoted by L, and the direction (azimuth or bearing) by Z. The sign of ∆X and ∆Y is determined by sin Z and cos Z. The rules on signs in the four quadrants must be strictly observed (see Section 1-2).