Traverse & Leveling Calculations Flashcards

Point A has coordinates N 5,432.18, E 3,217.45 and Point B has coordinates N 4,891.32, E 3,648.72. What is the departure (ΔE) from A to B?

Answer: +431.27 ft

Departure ΔE = E_B − E_A = 3,648.72 − 3,217.45 = +431.27 ft (eastward).

Using the same two points (A: N 5,432.18, E 3,217.45 and B: N 4,891.32, E 3,648.72), what is the horizontal distance AB?

Answer: 692.0 ft

Distance = √(ΔN² + ΔE²) = √(540.86² + 431.27²) = √478,523 ≈ 692.0 ft.

A course runs from point P (N 1,000.00, E 1,000.00) with a bearing of S 38°22' E and length 475.50 ft. What are the approximate coordinates of the endpoint?

Answer: N 627.2, E 1,295.1

Lat = −475.50 × cos(38°22') ≈ −372.8 ft; Dep = +475.50 × sin(38°22') ≈ +295.1 ft; endpoint ≈ N 627.2, E 1,295.1.

The 'inverse' computation in coordinate geometry refers to:

Answer: Computing the bearing and horizontal distance between two points of known coordinates

Inverse computation solves for the direction (bearing) and distance between two coordinate pairs — the reverse of the forward (direct) problem.

In a missing-line calculation, ΔN = −218.40 ft and ΔE = +163.70 ft. In which bearing quadrant does the line fall?

Answer: SE (S __° E)

Negative ΔN indicates a southward component; positive ΔE indicates an eastward component — the bearing is in the SE quadrant.

The Double Meridian Distance (DMD) of the FIRST course of a traverse equals:

Answer: The departure of the first course

By definition, the DMD of the first course equals its own departure; subsequent DMDs are computed by adding successive departures.

The coordinate (Gauss/shoelace) method computes double the polygon area using which formula?

Answer: 2A = Σ[Xₙ(Yₙ₊₁ − Yₙ₋₁)]

The shoelace formula states 2A = Σ[Xₙ(Yₙ₊₁ − Yₙ₋₁)], where coordinates are cycled through all polygon vertices.