In trigonometric leveling, when the distance D is known and the angle of elevation alpha is observed from instrument station A to target B, the difference in elevation is:
Choose the correct answer
D x cos(alpha)
D x tan(alpha) + hi - ht (where hi = instrument height, ht = target height)
D x sin(alpha)
D / tan(alpha)
Correct Answer
B. D x tan(alpha) + hi - ht (where hi = instrument height, ht = target height)
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Trigonometric leveling: h = D x tan(alpha) (for horizontal distance D), or S x sin(alpha) (for slope distance S). Full formula: elev_B - elev_A = D x tan(alpha) + hi - ht, where hi = height of instrument above A, ht = height of target above B. For long distances, curvature and refraction correction C = 0.0673 D^2 (km) in metres.
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