The height of an EDM set up at station A is 1.415 m. The height of the reflector set up at station B is 1.124 m. The height of the theodolite at station A used to measure the vertical angle is 1.623 m. The height of the target at station B on which the vertical angle sight is taken is 1.175 m. The measured vertical angle is 5° 32' 45" (upward). The slope distance, after meteorological corrections, is 1537.248 m. Determine the horizontal distance between stations A and B.
Question
The height of an EDM set up at station A is 1.415 m. The height of the reflector set up at station B is 1.124 m. The height of the theodolite at station A used to measure the vertical angle is 1.623 m. The height of the target at station B on which the vertical angle sight is taken is 1.175 m. The measured vertical angle is 5° 32' 45" (upward). The slope distance, after meteorological corrections, is 1537.248 m. Determine the horizontal distance between stations A and B.
Solution
To determine the horizontal distance between stations A and B, we need to first calculate the difference in height between the EDM setup and the target.
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Calculate the difference in height between the EDM setup and the target:
Height difference = (Height of EDM at A + Height of theodolite at A) - (Height of reflector at B + Height of target at B)
Height difference = (1.415 m + 1.623 m) - (1.124 m + 1.175 m)
Height difference = 0.739 m
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Convert the vertical angle to decimal degrees:
Vertical angle = 5° 32' 45" = 5 + 32/60 + 45/3600 = 5.54583333°
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Convert the vertical angle from degrees to radians:
Vertical angle in radians = 5.54583333° * (π/180) = 0.096775 radians
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Calculate the horizontal distance:
Horizontal distance = Slope distance * cos(vertical angle in radians) - Height difference
Horizontal distance = 1537.248 m * cos(0.096775 radians) - 0.739 m
Horizontal distance = 1533.68 m
So, the horizontal distance between stations A and B is approximately 1533.68 m.
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