Total-Station Slope-to-Horizontal Reduction
The right-triangle reduction of an EDM/total-station slope distance to horizontal distance and elevation: with a zenith angle Z, H = S sin Z and V = S cos Z; with a vertical angle a, H = S cos a and V = S sin a; ground-to-ground elevation difference = V + instrument height - reflector height. A 250 ft slope shot at an 86 deg zenith is 249.39 ft horizontal and 17.44 ft up. The step that feeds the horizontal distance to cogo-forward-point. No curvature/refraction or grid scale factor; the instrument and control govern.
Formula and source
zenith angle Z: H = S sin(Z), V = S cos(Z). vertical angle a: H = S cos(a), V = S sin(a). ground-to-ground elevation difference = V + instrument_height - reflector_height.
Standard plane-survey EDM/total-station slope reduction by right-triangle trigonometry, as compiled in the standard surveying references (Ghilani, Elementary Surveying), by name.
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