Traverse Departure

In surveying, a traverse line can be split into two perpendicular parts: north-south (latitude) and east-west (departure). This formula gives the east-west part by taking the line length and multiplying by the sine of the bearing angle, because sine returns the ratio of the opposite side to the hypotenuse in a right triangle. It works whenever the bearing is measured from the north-south reference so that the line forms a right triangle with the coordinate axes.

Use this when reducing a measured traverse course into coordinate components for plotting, checking closure, or computing station coordinates. It is common in land surveying, route alignment, and any fieldwork where you need how much a line moves east or west.

• Using cosine instead of sine for departure
• Forgetting that the sign depends on direction, not just the magnitude
• Mixing up bearings measured from north with angles measured from east