FW_3 - Laying Out and Measuring Lines and Angles by Tape

FW#3: LAYING OUT AND MEASURING LINES AND ANGLES BY TAPE

LAYING OUT AND MEASURING

Objective: To familiarize students with the use of a tape in measuring and laying out angles.

To familiarize students with the use of a tape in laying out perpendicular and parallel lines.

This is a group activity.

Instruments:

1 Steel Tape

Marking Pins

2 Range Poles

Site: UST Field / Benavides Park

Procedure:

Establishing Perpendicular Lines:

A. 3-4-5 Method

Given Line: XY

1. Establish line XY. Distance XY should be more than 5

meters.

2. Lay out a distance of 3 meters along line XY from

point A. Mark it with a marking pin an

point B.

3. From point A, lay out a distance of 4 meters; make a

loop at the end to have the exact full meter mark

and connect the other end of the tape to point with

a distance equal to 5 meters. Then mark the loop

point with marking pin and designate it as point C.

4. ∠ BAC should be equal to 90°. Check the accuracy

by measuring the angle laid.

5. Compute the relative precision.

B. Chord Bisection Method:

Given Line: JK

1. Establish line JK.

2. Hold firmly the zero end of the tape at point M.

3. Unwind the tape up to the length which is more than

sufficient to intersect the given line at two separate

points.

4. From point M, swing the tape and mark the points of

intersection with the given line. Designate them as points

N and O. Take note of the lengths of MN and MO.

5. Measure distance NO and mark the midpoint as point P.

6. ∠MPN and ∠MPO should be equal to 90°. Check the

accuracy by measuring the angle laid.

7. Compute the relative precision.

AND ANGLES BY TAPE

FIELDWORK # 3

NG OUT AND MEASURING LINES AND ANGLES BY TAPE

To familiarize students with the use of a tape in measuring and laying out angles.

familiarize students with the use of a tape in laying out perpendicular and parallel lines.

UST Field / Benavides Park

Given Point: A (along line XY)

Establish line XY. Distance XY should be more than 5

Lay out a distance of 3 meters along line XY from

point A. Mark it with a marking pin and call it as

From point A, lay out a distance of 4 meters; make a

end to have the exact full meter mark

and connect the other end of the tape to point with

distance equal to 5 meters. Then mark the loop

point with marking pin and designate it as point C.

BAC should be equal to 90°. Check the accuracy

FIGURE: Establishing Perpendicular Lines (3

Given Point: M (outside line JK)

Hold firmly the zero end of the tape at point M.

length which is more than

sufficient to intersect the given line at two separate

From point M, swing the tape and mark the points of

intersection with the given line. Designate them as points

hs of MN and MO.

Measure distance NO and mark the midpoint as point P.

MPO should be equal to 90°. Check the

accuracy by measuring the angle laid.

FIGURE: Establishing Perpendicular Lines

(Chord Bisection Method)

J

M

N

L2 = 4 meters

L1 = 3 meters

C

A X

L1

loop

L3 =

L3

L2

Page 1

familiarize students with the use of a tape in laying out perpendicular and parallel lines.

A (along line XY)

FIGURE: Establishing Perpendicular Lines (3-4-5 Method)

M (outside line JK)

Establishing Perpendicular Lines

(Chord Bisection Method)

K

M

O

3 meters Y B

= 5 meters


FORMULA:

Discrepancy = θ – Φ

Relative Precision = lDiscrepancyl

Mean Angle

Establishing Parallel Lines:

Given Line: DE

1. Establish line DE and point F.

2. At point F, hold the zero end of the tape.

3. Unwind the tape such that it is sufficient to intersect the given line.

4. Swing the tape until a whole meter tape m

marking pin and designate it as point F’

5. Mark also with marking pin the midpoint of the tape and designate it as point O.

6. Let one member hold the tape at point O. Transfer the two ends of

still at its original position. Designate the new point on the given line as point G’ and the new position of the

zero end as point G.

7. Measure lines FG’ and GF’.

FORMULA:

Discrepancy = Length FG’ – Length GF’

Mean Angle = θ + Φ

2

F

D G’

L2

AND ANGLES BY TAPE

where: θ = angle laid, 90°

Φ = angle measured

Given Point: F (outside line DE)

At point F, hold the zero end of the tape.

Unwind the tape such that it is sufficient to intersect the given line.

Swing the tape until a whole meter tape mark intersects the given line. Mark the point of intersection with

marking pin and designate it as point F’

Mark also with marking pin the midpoint of the tape and designate it as point O.

Let one member hold the tape at point O. Transfer the two ends of the tape in opposite directions with midpoint


FIGURE: Establishing Parallel Lines

Length GF’ or Discrepancy = Length 2 – Length 3

F G

E G’ F’

O

L1

L3

Page 2

F (outside line DE)

ark intersects the given line. Mark the point of intersection with

the tape in opposite directions with midpoint



A

A

L

L

φ

Laying out a given horizontal acute angle by tape.

1. Put a marking pin at any point on

2. From point A, lay out a 20-meter distance and mark the end with a marking pin and designate it as a point B.

3. From point A, lay out a distance of 20cosθ; make a loop at the end to hav

the other end of the tape to point with a distance equal to 20sinθ. Then mark the loop point with marking pin

and designate it as point C.

4. The angle laid is ∠ BAC which is equal to the given samp

5. Let θ = 30° for the first trial and 45° and 90° for the second and third trials respectively.

FORMULA:

Laying out angle:

AB = 20meters

BC = 20sinθ

AC = 20cosθ

Measuring a horizontal angle by chord bisection method:

1. Use the same angles laid from part 1.

2. Place the two range poles at points B and C.

3. With a certain distance from point A, say 8 meters, set points along lines AB and AC an

marking pins as points B’ and C’ respectively.

4. Measure the distance points B’ and C’.

5. Compute for ∠ BAC.

6. Repeat the same procedure for the 45° and 60° angles.

7. Compute the discrepancy and relative precision for each

Figure: Measuring horizontal angle.

φθ −=yDiscrepanc

Mean

• Instead of using mean angle in solving the relative precision, you may use the value of the given angle.

AND ANGLES BY TAPE

θ

20cosθ

20sinθ D=20m

loop

B

C

B’

A’

B

C

X

Laying out a given horizontal acute angle by tape.

Put a marking pin at any point on the ground. Call this as point A. This will be the vertex of the angle.

meter distance and mark the end with a marking pin and designate it as a point B.

From point A, lay out a distance of 20cosθ; make a loop at the end to have the exact full meter mark and connect


BAC which is equal to the given sample.

Let θ = 30° for the first trial and 45° and 90° for the second and third trials respectively.

Figure: Laying out horizontal angle.

Measuring a horizontal angle by chord bisection method:

Use the same angles laid from part 1.

Place the two range poles at points B and C.

With a certain distance from point A, say 8 meters, set points along lines AB and AC an

marking pins as points B’ and C’ respectively.

Measure the distance points B’ and C’.

Repeat the same procedure for the 45° and 60° angles.

Compute the discrepancy and relative precision for each trial.

Measuring angle:

L

x

BAC 2

2

1sin =∠

Where: x = chord distance (B’C’)

L = length of the tape swung

A = vertex of ∠ BAC

B’ and C’ = crossing points where the arc intersects

lines AB and AC

Φ = angle to be measured (

2_

φθ +=AngleMean

MeanAngle

yDiscrepancecisionlative =PrRe

Instead of using mean angle in solving the relative precision, you may use the value of the given angle.

Page 3

the ground. Call this as point A. This will be the vertex of the angle.

meter distance and mark the end with a marking pin and designate it as a point B.

e the exact full meter mark and connect


With a certain distance from point A, say 8 meters, set points along lines AB and AC and mark them with

L

x

2

chord distance (B’C’)

length of the tape swung

crossing points where the arc intersects

angle to be measured (∠ BAC)

Instead of using mean angle in solving the relative precision, you may use the value of the given angle.


Title: _______________________________

Group No.

Time Started:

Time Finished:

Actual Site:

GROUP MEMBERS

DATA & RESULTS:

Laying out horizontal angles:

D (meters)

θ (°)

AB (meters)

BC (meters)

AC (meters)

Measuring horizontal angles:

TRIAL 1

L (meters)

θ ( ° )

X or B’C’ (meters)

Φ ( ° )

Discrepancy ( ° )

Mean Angle ( ° )

Relative Precision

AND ANGLES BY TAPE

FIELDWORK REPORT # 3

Title: _______________________________

Yr. & Sec.:

Date Performed:

Date Submitted:

Weather Condition:

DUTY/IES

TRIAL 1 TRIAL 2

TRIAL 1 TRIAL 2

Page 4

TRIAL 2


3-4-

L1 (meters)

L2(meters)

L3 (meters)

θ (°)

Φ (°)

Discrepancy (°)

Mean Angle (°)

Relative Precision

DRAWING/S:

SOURCES OF ERRORS:

REMARK/S:

AND ANGLES BY TAPE

Establishing Perpendicular Lines Establishing Parallel Lines

-5 Method Chord Bisection Method

Page 5

Establishing Parallel Lines

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FW_3 - Laying Out and Measuring Lines and Angles by Tape