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TRIGONOMETRIC LEVELING Trigonometric leveling or indirect leveling is defined as the determination of differences in elevation from observed vertical angles and either horizontal or inclined distances. The figure below illustrates a typical setup for trigonometric leveling where the observed vertical angle is and the known horizontal and inclined distances, measured in meters, are d and s, respectively. The height of the instrument above point A is denoted as h.i., and the reading on the rod held at the distant point B is RR. The vertical distance, V, could be determined in two ways as follows: V = d tan or V = s sin Eq. (1) Eq. (2) The difference in elevation between A and B may be determined by any of the following equations DEab = V h.i. – RR Eq. (3) If the elevation of A is known, the elevation of B can then be determined as follows: Elev B = Elev A + DEab Eq. (4) When trigonometric leveling is employed in much longer sights, the slope distance is measured using EDM instruments and precise optical theodolites are utilized for measuring vertical angles. Also, the correction for the combined effects of curvature and refraction is added when the vertical angle is an upward sight; it is subtracted when downward sight is observed. That is Upward sight DEab = V + h.i. – RR + hcr Eq. (5) Downward sight DEab = V – h.i. – RR – hcr Elementary Surveying Notes of AM Fillone Eq. (6) Upward line of sight RR B s V D.E.ab h.i. A d Elev. B Elev. A Datum Downward line of sight d h.i. A s V DEab RR B Elev. A Elev. B Datum Elementary Surveying Notes of AM Fillone

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