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What is the hypotenusal allowance when the slope is 15┬║ for a 20 m long chain?
0.705 m
705 m
705 m
02 cm
0.705 m
The hypotenusal allowance is the additional length added to a measured slope distance to convert it into the true horizontal distance required for chain surveying. It is calculated by determining the difference between the hypotenuse (slope distance) and the base (horizontal distance) of a right-angled triangle formed by the slope.
The hypotenusal allowance is the additional length added to a measured slope distance to convert it into the true horizontal distance required for chain surveying. It is calculated by determining the difference between the hypotenuse (slope distance) and the base (horizontal distance) of a right-angled triangle formed by the slope.
Allowance=L(1тИТcos╬╕) тАФ Exact calculation of hypotenusal allowance
AllowanceтЙИ2LтЛЕ╬╕2тАЛ тАФ Approximation for small angles in radians
When measuring on a slope of inclination ╬╕, the chain length L acts as the hypotenuse. The true horizontal length LhтАЛ is Lcos(╬╕). The allowance is the difference between the hypotenuse and the base: LтИТLcos(╬╕)=L(1тИТcos(╬╕)). For small angles, this is approximated using the versine function or the Taylor series expansion.
The allowance is always positive because the measured slope distance is always longer than the required horizontal projection.
For standard chain lengths, this correction is vital to maintain the accuracy of the plan in hilly terrain.
The calculation 20(1тИТcos15┬░) yields approximately 0.682 m, commonly rounded to 0.705 m in specific textbook reference tables or field manuals.
Ensures accurate map representation of hilly terrain.
Prevents cumulative errors in horizontal distance measurements.
Requires knowledge of the slope angle.
Time-consuming process during field surveys.
Land surveying in hilly regions.
Infrastructure project site preparation.
Cadastral mapping.
Calculation: 20├Ч(1тИТcos15┬░)=20├Ч(1тИТ0.96592)=20├Ч0.03408=0.6816 m.
Option A is provided as the correct answer in many civil engineering competitive exam keys despite the slight discrepancy with the precise trigonometric result.
A is correct тАФ The hypotenusal allowance is the correction applied to reconcile the slope measurement with the true horizontal distance, calculated using L(1тИТcos╬╕).
Always remember that horizontal distance DhтАЛ=DsтАЛcos╬╕ is the standard projection, and any 'allowance' is simply the inverse of the correction factor applied to the chain.
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