Closed traverse with missing data: In a closed traverse, which of the following can be computed from the remaining measurements when one element is omitted?

Introduction / Context:

A closed traverse geometrically returns to its starting point. This closure condition enables recovery of missing data using coordinate computations when one side’s measurements are lost or omitted, provided the rest are reliable.

Given Data / Assumptions:

• Closed traverse with n sides; all sides except one have known lengths and bearings.
• Plane surveying assumptions; no geodetic curvature corrections needed for short traverses.
• Measurements are internally consistent or adjusted.

Concept / Approach:

Compute departures (D) and latitudes (L) of all known sides. Because ΣD = 0 and ΣL = 0 for a closed traverse, the unknown side must supply departures and latitudes equal to the negative of the sums of the known sides. From these (D_u, L_u), compute the unknown length and bearing: length = √(D_u² + L_u²) and bearing = arctan(D_u/L_u) adjusted to the proper quadrant.

Step-by-Step Solution:

Verification / Alternative check:

Plotting the traverse by independent coordinates will visually confirm that the computed side closes the figure accurately.

Why Other Options Are Wrong:

• Stating only length or only bearing underuses the closure conditions; both are determinable.
• Adjacent-side data alone are unnecessary if the rest of the traverse is known.
• ‘‘All the above’’ is incorrect because the single best statement is that both length and bearing can be found.

Common Pitfalls:

• Forgetting quadrant corrections when deriving bearings from departures/latitudes.

Final Answer:

both length and bearing of one side