185/3336–9FE Reference Handbook 10.4 · Surveying · Trigonometric Leveling

Handbook formula

Trigonometric Elevation Difference

Trigonometric leveling uses a slope distance and a vertical (or zenith) angle. Add the instrument height h_i and subtract the target (prism/rod) height h_t. Apply C+R on long sights. Total-station elevations are this formula internally.

Slope distance
Vertical angle from horizon
Zenith angle
Instrument and target heights
Elevation difference along the sight

Step-by-step solved example

S = 80.00 m, θ = +12°00', h_i = 1.55 m, h_t = 1.55 m. Point A elev = 100.00 m. Find elev_B.

θSH
Δh = S sinθ (or zenith complement).
  1. 1. Δh

    Δh = 80.00 sin 12° = 80.00 × 0.20791 = 16.63 m.

  2. 2. Heights cancel

    h_i = h_t so Elev_B = 100.00 + 16.63 = 116.63 m.

Answer: Elev_B = 116.63 m

10 practice questions

0/10 correct

1.S = 100 m, θ = 30°. Δh =

2.Zenith z = 80°, S = 200 m. Δh is nearest

3.If h_i > h_t on a horizontal sight (θ = 0), point B is

4.Negative vertical angle means point B is

5.S = 50.00 ft, θ = 8.00°, h_i = 5.12, h_t = 6.00, Elev_A = 820.00. Elev_B nearest

6.Trig leveling over 2 km should include

7.When h_i = h_t, Elev_B − Elev_A equals

8.A zenith of 90° with equal hi and ht gives ΔElev

9.Total station reports slope, H, and Δh using

10.S = 40 m, θ = −3°, hi = ht. Δh is nearest