Answer :
Final answer:
The corrected horizontal length is calculated by first correcting the slope distance for the tape's length discrepancy, and then applying a slope correction using the elevation difference. The corrected horizontal length is 736.034ft.
Explanation:
To find the corrected horizontal length of the line, we first need to calculate the slope length correction from the nominal length of the tape. Secondly, we will carry out a slope correction which reduces the slope length to its horizontal length. The tape's actual length is 99.9ft while its nominal length is 100ft, so the correction factor is 100/99.9 = 1.001001. The corrected slope distance is therefore 735.5ft * 1.001001 = 736.224ft.
Next, we use the elevation difference to calculate the slope correction. Here, we apply the Pythagorean theorem, which in this context is the square of the corrected slope distance (the hypotenuse) equals the square of the corrected horizontal distance (the base) plus the square of the vertical distance (the elevation). Solving for the base, we get: corrected horizontal distance = square root [(736.224ft)[tex]^{2}[/tex] - (11.5ft)[tex]^{2}[/tex]] = 736.034ft.
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