Question #259114

1. SLOPE TAPING. A measurement is made along a line that is inclined by a vertical angle of

15°25’ as measured using a hand level and clinometer. The slope measurement is 756.52m. What

is the corresponding horizontal distance?

2. CORRECTION OF TAPE LENGTH. The correct distance between points E and F is 213.50m. If a 100m tape that is 0.025m too long is used to measure EF, what will be the measured distance?

3. CORRECTION OF TAPE LENGTH. The sides of a square lot having an area of 2.25 hectares

were measured using 100m tape that was 0.04m too short. Compute the error in the area.

Expert's answer

**SLOPE TAPING.** A measurement is made along line that is inclined by a vertical angle of 15°25’ as measured using a hand level and clinometer. The slope measurement is 756.52m. What is the corresponding horizontal distance?

s= 756.52m

*α*= 15°25’

*d= s cosα*

*d*= (756.52)cos(15°25’)

d = 729.30m

**CORRECTION OF TAPE LENGTH.** The correct distance between points E and F is 213.50m. If a 100m tape that is 0.025m too long is used to measure EF, what will be the measured distance?

NL = 100m

Corr = 0.025m

ML = 213.50m

C_{1}= Corr(ML/NL)

= 0.025(213.50*m/*100m)

C_{1}= 0.053m

CL= ML + C_{1}

= 213.50m+ 0.053m

CL = 213.55m

**CORRECTION OF TAPE LENGTH.** The sides of a square lot having an area of 2.25 hectares were measured using 100m tape that was 0.04m too short. Compute the error in the area.

A_{s}= 2.25 hectares x (10000*m*^{2}/1 hectare)

A_{s}= 22,500 m^{2}

ML = √A_{s}

= √22,500m2

ML = 150m

NL = 100m

Corr = 0.04m(too short)

C_{1}= Corr(*ML/NL*)

= 0.04(150*m*/100*m*)

C_{1}= 0.06m

CL= ML-C1

= 150m -0.06m

CL = 149.94m

CA_{s}= (149.94m)^{2}

CA_{s}= 22482.0036m^{2}

Error in the area = 22,500 m^{2}-22482.0036m^{2}

Error in the area = 17.9964m^{2}

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