Slope Distance to Horizontal

H = S cos θ = S sin z

EDM and taping measure slope distance S. Horizontal distance H = S cos θ where θ is the vertical angle from the horizon, or H = S sin z if z is the zenith angle (z = 90° − θ). Never use slope distances as traverse lengths.

$S$: Slope (measured) distance
$H$: Horizontal distance
$θ$: Vertical angle from horizon
$z$: Zenith angle from vertical

Step-by-step solved example

Measured slope distance 150.00 ft at +8°00' vertical angle. Find H.

Horizontal distance H = S cosθ from a measured slope length.

1. Cosine
cos 8° = 0.990268.
$cos 8^{\circ} = 0.99027$
2. Horizontal
H = 150.00 × 0.99027 = 148.54 ft.
$H = 148.54 ft$

Answer: H = 148.54 ft

10 practice questions

0/10 correct

1.S = 100.00 m, θ = 0°. H =

2.S = 80.00 ft, θ = 60°. H =

3.Zenith angle z = 90° means the sight is

4.H = S sin z. If z = 80°, S = 200 m, H is nearest

5.A 2% grade is a vertical angle nearest

6.Using S instead of H in a traverse will

7.θ = −12° (downhill) vs +12° for the same S. H is

8.S = 50.000 m, θ = 5.00°. Correction S − H is nearest

9.EDM slope reduction also needs

10.Percent slope s% related to θ by