# Question: 1 41 the length of a line measured with a...

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1) 4.1 The length of a line measured with a 30-m tape is 310.550 m. When the tape is compared to the standard it is found to be 0.010 m too short under the same conditions of support, tension, at temperature as existed during measurement of the line. Compute the length of the line.

2) 4.5 A 30-m tape having a standard length of 30.005 m is to be used to lay out a building that has plan dimensions of 150.000 by 270.000 m. What horizontal measurements must be made on the ground in the field to perform this layout?

3) 4.6 The following slope distances and differences in elevations between the tape ends were recorded for a measurement:

Slope distance | Difference in elevation, m |
---|---|

30.005 | 1.452 |

29.950 | 3.500 |

30.000 | 0.505 |

25.989 | 2.445 |

10.345 | 1.595 |

Calculate the horizontal distance between the two endpoints of this line.

4) 4.16 A steel tape having a standardized length of 29.990 m, with 8 kg tension, at 20°C, and supported at the two ends, was used to measure a distance over smooth , level terrain using standard support and tension and at an average recorded temperature of 30°C. The recorded distance was 915.258 m. Determine the correct horizontal distance. The weight of the tape is 0.60 kg.

5) 4.20 A standardized 30-m tape weighing 0.7 kg measures 29.9935 m fully supported, with 8.0 of tension and at 20°C. (a) A horizontal distance of 3248.835 m is measured with the tape fully supported, with 8.0 kg of tension on full tape lengths (3.0 kg on the partial length) and at a temperature recorded at 8°C. Determine the correct horizontal distance. (b) A horizontal distance of 200.843 m is to be measured from a monument to set an adjacent property corner. What horizontal must be measured under standardization conditions of support and tension to set this property where the temperature is 21°C?

6) A 50-m tape of standard length has a weight of .05kg/m, with a cross-sectional area of 0.04 sq.cm. It has a modulus of elasticity of 2.10x106 kg/sq.cm. The tape is of standard length under a pull of 5.5 kg when supported throughout its length and a temperature of 20°C. This tape was used to measure a distance between A and B and was recorded to be 458.65m. long. At the time of measurement the pull applied was 8 kg. with the tape supported only at its end points and the temperatu-re observed was 18°C. Assuming coefficient of linear expansion of the tape is 0.0000116m/°C. Compute for the true length (with the combined effects of tension, sag and temperature) of the measured line AB. Plot (Illustrate) the following:

7) 6.3 The following azimuths are from the north: 329°20’, 180°35’, 48°32’, 170°30’, 145°25’, 319°35’, 350°45’, 95°49’, 11°30’, 235°45’. Express these directions as (a) azimuth from the south, (b) back azimuths, (c) bearings.

8) 6.7 The following azimuths are reckoned from the north: FE = 4°25’, ED = 90°15’, DC = 271°32’, CB = 320°21’, and BA = 190°45’. What are the corresponding bearings? What are the deflections angles between consecutive lines?

9) 6.8 The interior angles of a five-sided closed polygon ABCDE are as follows: A, 120°24’; B, 80°15’; C, 132°24’; D, 142°20’. The angle E is not measured. Compute the angle at E, assuming the given values to be correct.’

10) 6.11 In an old survey made when the declination was 4°15’E, the magnetic bearing of a given line was N35°15’E. The declination in same locality is now 1°10’W. What are the true bearing and the present magnetic bearing that would be used in retracing the line?

11) The following bearings taken on a closed compass and fill up the table.

Lines | Bearings (deg-min) | Azimuth N | Deflection Angles | Angle to the Right | Interior Angles |
---|---|---|---|---|---|

AB | S 37-30 E | ? | 83°45’ | 163°45’ | ? |

BC | S 43-30 W | ? | ? | ? | ? |

CD | N 73-30 W | ? | ? | ? | ? |

DE | N 11-45 E | ? | ? | ? | ? |

EF | ? | ? | ? | ? | ? |

12) ILLUSTRATE THE TRAVERSE AND SHOW THE SOLUTIONS. Transform graphically into a figure with sides containing unknown quantities are made adjoining. Determine the unknown quantities.

Course | Length | Bearing |
---|---|---|

AB | 492.98 | N 05°30’ E |

BC | UNKNOWN | S 12°17’ E |

CD | 845.85 | N 46°03’ E |

DE | 852.18 | S 67°24’ E |

EF | 1210.50 | UNKNOWN |

FA | 661.26 | N 55°27’ W |

AB BC CD DE EF FA

13) ILLUSTRATE THE TRAVERSE AND SHOW THE SOLUTIONS. Transform graphically into a figure with sides containing unknown quantities are made adjoining. Determine the unknown quantities.

Course | Length | Bearing |
---|---|---|

AB | 249.18 | S 19°32’ E |

BC | UNKNOWN | N 74°09’ E |

CD | 445.10 | S 36°40’ E |

DE | 668.27 | S 51°14’ W |

EF | 866.79 | N 73°25’ W |

FG | UNKNOWN | N 26°00’ W |

GA | 560.15 | N 64°32’ E |

14) Given Below is the technical description of lot 2061, Cebu Cadastre.

Line | Length (m) | Azimuth from South |
---|---|---|

1-2 | 22.04 | S 32°17’ W |

2-3 | 10.00 | N 36°35’ W |

3-4 | 5.00 | N 15°47’ W |

4-1 | 19.95 | N 73°07’ E |

1. Find the area of the lot by DMD method. 2. Find the area of the lot by DPD method.

15) Compute for the following and show the tabulated solutions: (Notes: Use 2 decimal places for all corrections and lengths, degrees and minutes for angles)

Line | Length (m) | Azimuth from South |

AB | 1020.87 | 168°35’ |

BC | 1117.26 | 263°30’ |

CD | 660.08 | 304°25’ |

DE | 495.85 | 5°30’ |

EF | 850.62 | 46°15’ |

FA | 855.45 | 112°30’ |

1. Using Compass Rule, solve for adjusted latitudes, departures, distances and bearings for all the traverse lines

2. Using Transit Rule, solve for adjusted latitudes, departures, distances and bearings for all the traverse lines

3. Using coordinate method and using the result of balancing traverse in # 2 (transit rule) with station A (N,E) coordinates = (20000, 20000), solve for the coordinates (N, E) of all traverse stations and the area of the traverse

4. Using DMD method and using the result of balancing traverse in # 2 (transit rule), solve for area of the traverse

5. Using DPD method and using the result of balancing traverse in # 2 (transit rule), solve for area of the traverse

16) At regular interval of 5 meters along line AB, the measured offset distances from the line AB to the edge of the stream are: 6.5, 7.3, 12.1, 12.7, 14.5, 16.0, 18.6, 18.5, 16.4, 15.9, 14.7, 13.5, 12.75, 12.5, 9.7 and 2.0. What is the area between line AB and the stream?

1. Area using trapezoidal rule

2. Area using Simpson’s 1/3 rule