A slope distance of 165.360 m (corrected for meteorological conditions) was measured from A to B, whose elevations were 447.401 and 445.389 m above datum, respectively. Find the horizontal length of line AB if the heights of the EDM instrument and reflector were 1.417 and 1.615 m above their respective stations. (
Question
A slope distance of 165.360 m (corrected for meteorological conditions) was measured from A to B, whose elevations were 447.401 and 445.389 m above datum, respectively. Find the horizontal length of line AB if the heights of the EDM instrument and reflector were 1.417 and 1.615 m above their respective stations. (
Solution
To find the horizontal length of line AB, we first need to find the difference in elevation between points A and B, and then subtract the heights of the EDM instrument and reflector from this difference.
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Find the difference in elevation between points A and B: Elevation difference = Elevation of A - Elevation of B Elevation difference = 447.401 m - 445.389 m = 2.012 m
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Subtract the heights of the EDM instrument and reflector from the elevation difference: Corrected elevation difference = Elevation difference - (Height of EDM instrument + Height of reflector) Corrected elevation difference = 2.012 m - (1.417 m + 1.615 m) = -1.02 m
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The slope distance is the hypotenuse of a right triangle, where the horizontal length of line AB is one side and the corrected elevation difference is the other side. We can use the Pythagorean theorem to find the horizontal length of line AB: (Slope distance)^2 = (Horizontal length)^2 + (Corrected elevation difference)^2 Solving for Horizontal length gives: Horizontal length = sqrt((Slope distance)^2 - (Corrected elevation difference)^2) Horizontal length = sqrt((165.360 m)^2 - (-1.02 m)^2) Horizontal length = sqrt(27324.1296 m^2 - 1.0404 m^2) Horizontal length = sqrt(27323.0892 m^2) Horizontal length = 165.297 m
So, the horizontal length of line AB is approximately 165.297 m.
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