Surveying – Latitude of a Traverse Leg (Reduced Bearing Method) In plane surveying with a closed traverse, the latitude (northing or southing) of a traverse leg is computed by multiplying the measured length of that leg by which trigonometric function of its reduced bearing?

Introduction:
Traverse computation converts field measurements (lengths and bearings) into rectangular components called latitude (north–south) and departure (east–west). This question checks whether you recall the exact trigonometric relation between a side's reduced bearing and its latitude component.

Given Data / Assumptions:

• Each traverse leg has a measured length L and a reduced bearing θ (0°–90° within its quadrant).
• Latitude is the projection of L on the north–south axis; departure is the projection on the east–west axis.
• Plane surveying assumptions apply (small area, neglecting curvature).

Concept / Approach:

Resolve the traverse side into orthogonal components using basic trigonometry. The component along the meridian (latitude) equals L * cos θ, while the component along the perpendicular (departure) equals L * sin θ. Signs (N/S and E/W) come from the quadrant of the reduced bearing, not from the magnitude formula itself.

Step-by-Step Solution:

Verification / Alternative check:

Check a limiting case: if θ = 0° (bearing exactly north/south), cos θ = 1 so latitude = L and departure = 0, which is consistent with geometry.

Why Other Options Are Wrong:

Tangent/cosecant do not represent orthogonal projections; 'sign of bearing' is not a magnitude; sine corresponds to departure, not latitude.

Common Pitfalls:

Swapping sine and cosine for latitude/departure; forgetting to apply the correct algebraic sign from the quadrant.

Final Answer:

Cosine of its reduced bearing