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.
S
Slope distance
θ
Vertical angle from horizon
z
Zenith angle
hi,ht
Instrument and target heights
Δh
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.
Δh = S sinθ (or zenith complement).
1. Δh
Δh = 80.00 sin 12° = 80.00 × 0.20791 = 16.63 m.
Δh=16.63m
2. Heights cancel
h_i = h_t so Elev_B = 100.00 + 16.63 = 116.63 m.
ElevB=116.63m
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