Reprinted with permission from Professional Publications, Inc., 1001 Solved Surveying Fundamentals Problems, 2nd ed., by Jan Van Sickle, Copyright 1997 by Professional Publications, Inc. Page 1-103 Problem 111 What relative error is the closest to that which would be the result of an angular error of 20”? (A) 1 part in 100,000 (B) 1 part in 20,000 (C) 1 part in 5,000 (D) 1 part in 10,000 Page 1-83 Problem 93 A right-of-way, 100.00 ft wide, crosses a lot, as shown in the following illustration. What is the area, in acres, within the right –of-way?

(A) 1.01 ac (B) 0.88 ac (C) 0.73 ac (D) 0.92 ac Page 1-77 Problem 88 Which of the four-sided figures described contains an area of 1 ac? (A) a square that is 209.10 ft on one side

(B) a rectangle that is 2 chains by 5 chains (C) a square that is 10 chains on a side (D) both B and C

Page 1-59 Problem 67 What is the area, in square feet, of the segment included in a curve with a radius of 52.46 ft and a central angle of 23°42’? (A) 268.50 sq ft (B) 16.10 sq ft (C) 20.89 sq ft (D) 276.41 sq ft

Page 5-5 Problem 9 The chain has been the standard unit of length in the Public Land Surveying System since its beginning and is still the standard prescribed by law. One of the reasons for its durability is its convenient relationship with the description of land in acres. Which of the following equations correctly describes this relationship? (A) 1 sq chain = 1 ac

(B) 80 sq chains = 40 ac (C) 10 sq chains = 1 ac (D) 100 sq chains = 1 ac

Page 5-6 Problem 11 Early field notes from public land surveys sometimes refer to a two-pole chain. What is a two-pole chain? (A) A two-pole chain is a chain that is equipped with two long wooden handles.

(B) The phrase two-pole chain is simply another term used to describe a standard length Gunter’s Chain. (C) A two-pole chain is 132.0 ft long. (D) A two-pole chain is one-half of a standard Gunter’s chain, or 33.00 ft long.

Page 5-7 Problem 13 Which of the following lengths is equivalent to 79.52 chains? (A) 1600.00 m (B) 5248.32 ft (C) 320.00 rods (D) 1920.41 varas Page 6-5 Problem 10 A line observed in 1911 had a magnetic bearing of N 10°24’ E, and the magnetic declination at that time was 04°E. What will the magnetic bearing of the line be today if the declination is 00°25’W? (A) N 14°31’ E (B) N 05°59’ E (C) N 09°50’ E (D) N14°49’ E Page 6-14 Problem 27 How far must the top of a fully extended 13.00 ft rod deviate from plumb to cause an error of +0.02 ft in a 7.00 rod reading? (A) 0.98 ft (B) 0.51 ft (C) 0.23 ft (D) 1.06 ft

Page 6-19 Problem 30 Given the following two observations, what are the rod readings in each case? Are the rods an equal distance from the observer?

(A) rod 1 = 5.35 rod 2 = 5.64 The rods are an equal distance from the observer. (B) rod 1 = 5.21 rod 2 = 5.54 The rods are an unequal distance from the observer. (C) rod 1 = 5.21 rod 2 = 5.53 Rod 1 is closer to the observer than rod 2. (D) rod 1 = 5.53 rod 2 = 5.21 Rod 1 is closer to the observer than rod 2. Page 6-39 Problem 54 A steel tape that is 100.00 ft long when supported only at its ends under a tension of 20 lb is used to measure a line. The temperature is 68°F, the pull on the tape is 40 lb, and the line is measured as 469.40 ft. The tape used is 0.33-in wide x 0.02 thick. If one assumes the modulus of elasticity of steel to be 29,000,000 psi, what is the length of the measured line? (A) 469.45 ft (B) 469.42 ft (C) 469.36 ft (D) 469.39 ft

Page 8-16 Problem 29 What flight height would be required to produce vertical photographs with a scale of 1:12,000 over level terrain if the average elevation is 3,300 ft and the focal length of the camera is 8 in? (A) 10,000 ft (B) 15,300 ft (C) 11,300 ft (D) 8,200 ft Page 8-17 Problem 30 The length of a one-story building is measured as 3.52 in on a vertical photograph. A map, which has a scale of 1:24,000, shows the same building as having a length of 2.67 in. What is the engineer’s scale of the photograph? (A) 1 in = 2400 ft (B) 1 in = 1136 ft (C) 1 in = 4321 ft (D) 1 in = 1517 ft Page 9-1 Problem 1 Which of the following statements correctly describes the origin of the North American Datum (NAD) of 1927? (A) The origin of NAD 27 is at Meades Ranch in Kansas. (B) The origin of NAD 27 is geocentric. (C) The geoidal height of the origin of NAD 27 is assumed to be zero. (D) Both A and C are true. Page 10-4 Problem 6 The legend of a map indicates that its scale is 1:24,000. What name is usually given to this type of expression of scale? (A) an engineer’s scale (B) a graphical scale (C) a manuscript fraction (D) a representative fraction or scale ratio Page 10-4 Problem 7 Which of the following scale is closest to 1 in = 1 mi? (A) 1/62,500 (B) 1/24,000 (C) 1/100,250 (D) 1/63,360

Page 10-5 Problem 9 What is the representative fraction or scale ratio for 1 cm = 500m? (A) 1:50,000 (B) 1:254 (C) 1:5,000 (D) 1:24,000 Page 10-6 Problem 10 A map prepared for an engineering project has a scale of 1 in = 100 ft. A map prepared for a land subdivision has a scale of 1 in = 1 mi. Which of the following statements is true? (A) Both maps have a large scale. (B) The engineering map has the smaller scale of the two. (C) Both maps have a small scale. (D) The engineering map has the larger scale of the two. Page 10-8 Problem 14 In an area of a topographic map where the contour lines are equally spaced, a straight line crosses several contour lines. A consistent distance of 0.22 in is scaled on the map between each intersection of the straight line and the successive contour lines. If the scale of the map is 1:24,000 and the contour interval is 20 ft, what is the slope of the line? (A) 4.55% (B) 0.38% (C) 2.47% (D) 3:1 Page 10-9 Problem 15 What sort of topographic feature is indicated by the illustration shown?

(A) a lake or pond (B) a tailings pile (C) a glacier (D) a depression

Page 2-14 Problem 15 An existing rectangular parcel of land was measured many years ago with a Gunter’s chain and was found to contain 40 ac. The original surveyor noted later that the chain used to make the measurements was one link too short. Assuming that the error was evenly distributed throughout the measuring, what was the area of the parcel? (A) 39.60 ac (B) 39.20 ac (C) 40.80 ac (D) 40.40 ac Page 2-5 Problem 5 The owner of a rectangular parcel that is 50 ft by 200 ft wishes to double the area of the lot. She wants to acquire a strip of land to add to the end of the lot and another strip of exactly the same width to add to the side of the lot. Which of the following widths will accomplish the goal? (A) 40.00 ft (B) 37.12 ft (C) 52.76 ft (D) 35.07 ft Page 1-77 Problem 89 A property owner wishes to have a lot created from his property that is exactly square and contains 3 ac. What should be the dimension of one side of the square, in feet? (A) 208.71 ft (B) 290.80 ft (C) 295.16 ft (D) 361.50 ft

Page 1-56 Problem 62 What is the bearing of the long chord and its length for the curve in the preceding illustration? (Hint: points 1, 2, and 3 all lie on the curve. 1 and 3 are the endpoints of the curve)

(A) N 49°09’42” E and 485.86 ft (B) N 49°09’42”E and 478.43 ft (C) N 40°19’00” E and 478.43 ft (D) N 57°43’00” E and 485.86 ft Page 1-9 Problem 14 An instrument is 377.14 ft , measured horizontally, from the center of the base of a high-power transmission line tower. The reading at the center, on a vertical rod, taken with the telescope of the instrument level is 6.32 ft. The vertical angle measured to the top of the tower is 11°58’35”. What is the height of the tower? (A) 80.00 ft (B) 73.68 ft (C) 96.32 ft (D) 83.62 ft

 

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Page 2 of 9  

Page 1-4 Problem 22 A part of an old deed reads, “to an iron buggy axle; thence N8515’E, 18 chains and 86 links to a wooden stake; thence S0230’E, 16 chains and 98 links to a 3 in diameter iron pipe.” The wooden stake has decayed. Current measurements yield the following coordinates. iron buggy axle 7631.413N 5723.610E 3 in iron pipe 6615.016N

7012.813E The decision was made to define the position of the decayed wooden stake by relying on the distance alone. Which coordinate would correspond to the position of the stake under these conditions?

(A) 6401.105 N 5912.738E

(B) 6512.043N 5774.562E

(C) 7734.634N 6964.083E

(D) 8223.869N 7509.105E

Page 1-4 Problem 25 After all measurements for a survey have been completed, it is important to determine the height of the top of a tower with respect to the instrument used to observe it. The only available information is the actual height of the tower, 157 ft, and the two vertical angles observed. The vertical angle to the base of the tower is 0146’52”. The vertical angle to the top of the tower is 0950’33”. What is the vertical distance from the instrument to the top of the tower? Ignore the effects of the curvature and refraction in the solution.

(A) 188.08 ft (B) 191.29 ft (C) 191.38 ft (D) 205.34 ft

Page 1-5 Problem 28 The triangle shown contains 1.5 acres. It is an oblique triangle in which angle B is 10203’50”, angle A is 4756’10”, and angle C is 3000’00”.

What is the length of the side opposite angle C?

(A) 300.00 ft (B) 375.99 ft (C) 460.43 ft (D) 586.75 ft

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Page 1-16 Problem 74 The find the area between a straight fence and the bottom of a dry gulch, stationing was established along the fence and perpendicular offsets measured from them to the bottom of the ravine. All of the given distances were measured to the nearest foot.

What is the area, in acres, between the fence and the bottom of the ravine?

(A) 1.9 ac (B) 2.7 ac (C) 3.2 ac (D) 3.6 ac

Page 1-17 Problem 80 Two level cross sections a full station (100 ft) apart have center heights of 3.60 ft and 4.80 ft, respectively. Both cross sections are in cut and the base width of the designed roadway is 44.00 ft. The side slopes are 1½:1. What is most nearly the volume between these cross sections calculated by the average end area method?

(A) 780 yd3 (B) 900 yd3 (C) 950 yd3 (D) 1000 yd3

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Page 1-17 Problem 81.1 The following illustration represents data returned from the setting of slope stakes along a proposed road. All dimensions are in feet.

Width of the roadbed = 66 ft Side slope ratior = 3:1 1+10 C9.8 C1.0 C0.5 62.40 0.00 34.50 1+20 C10.0 C2.5 C1.8 63.00 0.00 38.40 What is the cross-sectional area indicated at stations 1+10 and 1+20, respectively?

(A) 193.56 ft2 and 245.13 ft2 (B) 218.40 ft2 and 321.45 ft2 (C) 270.99 ft2 and 363.04 ft2 (D) 285.93 ft2 and 308.71 ft2

Page 1-18 Problem 82 The calculation of a closed traverse reveals that the closing coordinates of the station from which the traverse began do not match the coordinates assigned to it at the beginning of the calculation. The coordinates are in feet. N 5000.000 E 10,000.000 (coordinates assigned at the beginning) N 5000.324 E 9999.871 (closing coordinates at the same station) Which of the following answers correctly represents the linear error of closure of the traverse and its direction?

(A) 0.349 ft, N2142’36”W (B) 0.453 ft, N3129’12”E (C) 0.698 ft, N6817’24”E (D) 0.929 ft, N2031’46”W

Page 1-18 Problem 85 The sum of the exterior angles of a closed plane traverse with eight sides has a theoretically correct value. What is that value?

(A) 1080 (B) 1440 (C) 1620 (D) 1800

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Page 1-19 Problem 89 The interior angles of a closed traverse of six sides are given. 11815’58”

9359’01” 2344’10” 26921’00” 9800’39” 11638’12”

Each angle has been measured with equal precision. Which of the following angles would be the correct adjusted value for the first angle?

(A) 11815’48” (B) 11815’58” (C) 11816’08” (D) 11816’15”

Page 1-20 Problem 97 Occupying point B at the easterly end of a line AB that bears S8956’15”E, a deflection angle of 0004’15” is turned to the left to point C. Occupying point C, a deflection angle of 0000’35” is turned to the right to point D. What is the azimuth from north of line CD?

(A) 8956’15” (B) 8959’55” (C) 9000’00” (D) 9000’05”

Page 1-21 Problem 105 The following field data have been used to set a slope stake. The width of the roadway is 60 ft and the side slopes are 1½:1. The elevation of the subgrade is 609.45 ft. HI = 618.23 ft ground rod = 7.3 ft What is the most nearly the distance from the center of the roadway to the slope stake?

(A) 30 ft (B) 32 ft (C) 34 ft (D) 36 ft

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Page 2-3 Problem 15 An existing rectangular parcel of land was measured many years ago with a Gunter’s chain and was found to contain 40 ac. The original surveyor noted later that the chain used to make the measurements was one link too short. Assuming that the error was evenly distributed throughout the measuring, what was the area of the parcel?

(A) 39.20 ac (B) 39.60 ac (C) 40.40 ac (D) 40.80 ac

Page 2-6 Problem 26.1 According to the illustration below:

A vertical curve must begin at the center of manhole 1 (sta 44+00, elev 741.25 ft) and end at manhole 2 (sta 52+72.43, elev 737.25 ft) as illustrated. The entering grade of -4% and the exiting grade of +3% cannot be changed. At what distance from manhole 1 will the grade -4% intersect the grade +3% from manhole 2?

(A) 429 ft (B) 431 ft (C) 440 ft (D) 441 ft

Page 2-7 Problem 26.3 According to the illustration below:

What are the stations and elevations of the PVIs of the vertical curves that make up the asymmetrical vertical curve illustrated?

(A) sta 41+23.25, elev 728.32 ft sta 49+41.36, elev 727.32 ft

(B) sta 46+15.50, elev 732.63 ft sta 50+51.715, elev 730.63 ft

(C) sta 48+31.00, elev 724.01 ft sta 41+23.25, elev 728.32 ft

(D) sta 48+31.00, elev 724.01 ft sta 49+41.36, elev 727.32 ft

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Page 2-10 Problem 37.9 Considering the curve illustrated, assume that Rc is equal to 955.00 ft, the I angle is 40, and the distance CA is 6.95 ft. What is the external distance labeled E?

(A) 64.18 ft (B) 68.69 ft (C) 70.85 ft (D) 72.33 ft

Page 5-10 Problem 43.2 Section 6 is part of a township where the normal closing distance occur on the northern and western boundaries of the township. What is the measurement implied by the information given in the illustration for the distance labeled E?

(A) 19.16 chains (B) 19.96 chains (C) 20.08 chains (D) 20.11 chains

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Page 5-26 Problem 107.1 What is the record area of lot 10?

(A) 35.60 ac (B) 35.71 ac (C) 36.21 ac (D) 40.00 ac

Page 6-5 Problem 29

Which of the following series of numbers would correctly replace those indicated by the letters X, Y, and Z on the field notebook page shown?

(A) X = 216.21 Y = 2.09 Z = 5.51

(B) X = 217.38 Y = 3.51 Z = 5.31

(C) X = 217.38 Y = 4.65 Z = 5.51

(D) X = 230.38 Y = 3.12 Z = 4.10

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Page 6-8 Problem 39 A level is set up between a BM and a turning point (TP) with the foresight and backsight balanced. The elevation of the BM at the backsight is 4107.22 ft, and the reading on the rod is 1.47 ft. The reading on the rod at the foresight is 4.69 ft. If the rod at the foresight was inclined toward the instrument by 15 at the moment it was read, what is the elevation of the TP?

(A) 4103.84 ft (B) 4104.00 ft (C) 4104.16 ft (D) 4104.32 ft

Page 6-16 Problem 84.3 What is the standard deviation of a single measurement calculated from the list of azimuths given, expressed to the nearest tenth of a second? 5918’37” 5918’47” 5918’22” 5918’22”

5918’24” 5918’27” 5918’34” 5918’25”

5918’21” 5918’49” 5918’27” 5918’19”

5918’26” 5918’21” 5918’39” 5918’20”

5918’17” 5918’26” 5918’40” 5918’10”

5918’30” 5918’27” 5918’49” 5918’46”

5918’23” 5918’22” 5918’37” 5918’41”

(A) ±0.8” (B) ±2.0” (C) ±5.9” (D) ±10.5”

Page 8-5 Problem 34 A distance between two road intersections on a vertical photograph is 5.12 in. The same distance on a map with a scale of 1:24,000 measures 3.00 in. The elevation of the essentially level terrain in the area is 1200 ft above sea level. If the focal length of the lens in the camera used to make the photograph was 6 in, what was the altitude of the aircraft above sea level when the photograph was taken?

(A) 7197 ft (B) 8230 ft (C) 12,000 ft (D) 14,060 ft

Page 10-2 Problem 8 A map’s legend shows that it has a scale of 1:62,500. A measurement between two features on the map is read as 27.20 on a scale that is incremented at 20 parts/in. Approximately what distance does the measured length represent on the ground?

(A) 7100 ft (B) 14,000 ft (C) 17,000 ft (D) 170,000 ft