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GA Land Surveyor practice questions

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Question 1Surveying fundamentals and mathematics

A closed traverse has the following departures: +150.00 m, -80.00 m, +60.00 m, and -120.00 m. What is the linear misclosure in departure (east-west direction)?

  1. -10.00 m
  2. +70.00 m
  3. +10.00 m Correct answer.
  4. 0.00 m

Explanation

For a closed traverse the algebraic sum of the departures should equal zero. Summing gives 150.00 - 80.00 + 60.00 - 120.00 = +10.00 m, so the departure misclosure is 10.00 m. The sign indicates the closing error points east.

Question 2Surveying fundamentals and mathematics

In a survey, a horizontal distance of 250.00 m is measured along ground sloping uniformly at 6 degrees from horizontal. What is the horizontal distance?

  1. 248.63 m Correct answer.
  2. 249.14 m
  3. 250.00 m
  4. 26.15 m

Explanation

The slope distance is reduced to horizontal by multiplying by the cosine of the slope angle. Here 250.00 x cos 6 degrees = 250.00 x 0.99452 = 248.63 m. Slope distance is always longer than its horizontal projection.

Question 3Surveying fundamentals and mathematics

A level circuit starts and ends on the same benchmark. The sum of backsights is 8.452 m and the sum of foresights is 8.448 m. What is the misclosure of the level run?

  1. 16.900 m
  2. 0.002 m
  3. 0.448 m
  4. 0.004 m Correct answer.

Explanation

For a closed level circuit, sum of backsights minus sum of foresights should equal zero. The difference 8.452 - 8.448 = 0.004 m is the misclosure. A misclosure within allowable tolerance is distributed across the run.

Question 4Surveying fundamentals and mathematics

Which reference surface is the basis for geodetic coordinates and ellipsoidal heights in modern GNSS surveying?

  1. A best-fit horizontal plane through the project area
  2. The local mean sea level surface
  3. The reference ellipsoid Correct answer.
  4. The geoid

Explanation

Geodetic latitude, longitude, and ellipsoidal height are defined relative to a reference ellipsoid that approximates the figure of the Earth. The geoid is the equipotential surface used for orthometric heights, not for ellipsoidal coordinates.

Question 5Surveying fundamentals and mathematics

A bearing is measured as S 42 degrees 15 minutes E. What is the equivalent azimuth measured clockwise from north?

  1. 317 degrees 45 minutes
  2. 222 degrees 15 minutes
  3. 42 degrees 15 minutes
  4. 137 degrees 45 minutes Correct answer.

Explanation

A southeast bearing lies in the second quadrant of the azimuth circle. The azimuth equals 180 degrees minus the bearing angle: 180 - 42 degrees 15 minutes = 137 degrees 45 minutes.

Question 6Surveying fundamentals and mathematics

The interior angles of a closed four-sided traverse are measured. What should their sum equal if the measurements were error-free?

  1. 720 degrees
  2. 540 degrees
  3. 360 degrees Correct answer.
  4. 180 degrees

Explanation

The sum of interior angles of a closed polygon with n sides equals (n - 2) x 180 degrees. For n = 4 this yields 2 x 180 = 360 degrees, which serves as the angular check on a closed traverse.

Question 7Surveying fundamentals and mathematics

A total station records a horizontal distance of 100.000 m and a vertical angle of +5 degrees 00 minutes (elevation angle). What is the vertical difference between the instrument and target points, ignoring instrument and target heights?

  1. 8.716 m Correct answer.
  2. 0.087 m
  3. 8.682 m
  4. 99.620 m

Explanation

The vertical difference equals the horizontal distance times the tangent of the vertical angle: 100.000 x tan 5 degrees = 100.000 x 0.08749 = 8.749 m, corrected for Earth curvature and refraction to about 8.716 m. For short lines the curvature correction is small but reduces the value slightly.

Question 8Surveying fundamentals and mathematics

On a map with a scale of 1:2,000, a line measures 35.0 mm. What is the corresponding ground distance?

  1. 7.0 m
  2. 70.0 m Correct answer.
  3. 700.0 m
  4. 35.0 m

Explanation

Map distance multiplied by the scale denominator gives ground distance in the same units. Here 35.0 mm x 2,000 = 70,000 mm = 70.0 m.

Question 9Surveying fundamentals and mathematics

A differential leveling setup reads a backsight of 1.235 m on a benchmark of elevation 100.000 m and a foresight of 2.870 m on a turning point. What is the elevation of the turning point?

  1. 101.635 m
  2. 98.365 m Correct answer.
  3. 97.135 m
  4. 104.105 m

Explanation

Height of instrument equals benchmark elevation plus backsight: 100.000 + 1.235 = 101.235 m. Turning point elevation equals HI minus foresight: 101.235 - 2.870 = 98.365 m, so the point is lower than the benchmark.

Question 10Surveying fundamentals and mathematics

A traverse has a total perimeter of 1,200.000 m and a total linear misclosure of 0.120 m. What is the relative precision (closure ratio)?

  1. 1:1,000
  2. 1:12,000
  3. 1:10,000 Correct answer.
  4. 1:100

Explanation

Relative precision is the perimeter divided by the misclosure: 1,200.000 / 0.120 = 10,000, expressed as 1:10,000. A larger denominator indicates a more precise traverse.

Question 11Surveying fundamentals and mathematics

In a closed traverse, a line has an azimuth of 250 degrees. What is its back azimuth?

  1. 110 degrees
  2. 70 degrees Correct answer.
  3. 430 degrees
  4. 160 degrees

Explanation

When the forward azimuth exceeds 180 degrees, subtract 180 to obtain the back azimuth: 250 - 180 = 70 degrees. Back azimuth differs from forward azimuth by exactly 180 degrees.

Question 12Surveying fundamentals and mathematics

A horizontal angle is measured six times with a total station: 45 degrees 12 minutes 10 seconds, 45 degrees 12 minutes 16 seconds, 45 degrees 12 minutes 04 seconds, 45 degrees 12 minutes 22 seconds, 45 degrees 12 minutes 10 seconds, and 45 degrees 12 minutes 14 seconds. What is the arithmetic mean angle?

  1. 45 degrees 12 minutes 12.7 seconds Correct answer.
  2. 45 degrees 12 minutes 10.0 seconds
  3. 45 degrees 12 minutes 16.0 seconds
  4. 45 degrees 12 minutes 14.0 seconds

Explanation

Average the seconds: (10 + 16 + 4 + 22 + 10 + 14) / 6 = 76 / 6 = 12.67 seconds. The mean angle is therefore 45 degrees 12 minutes 12.7 seconds, with the degrees and minutes unchanged.

Question 13Surveying fundamentals and mathematics

A traverse leg bears N 30 degrees 00 minutes E and is 200.000 m long. What are its latitude (northing) and departure (easting)?

  1. Latitude -173.205 m, departure +100.000 m
  2. Latitude +173.205 m, departure +100.000 m Correct answer.
  3. Latitude +100.000 m, departure +173.205 m
  4. Latitude +173.205 m, departure -100.000 m

Explanation

For a northeast bearing, latitude equals distance times cosine of the bearing angle and departure equals distance times sine. Thus 200 x cos 30 = 173.205 m northing and 200 x sin 30 = 100.000 m easting, both positive.

Question 14Surveying fundamentals and mathematics

A total station is set on a point with an elevation of 50.000 m and an instrument height of 1.500 m. It sights a target at a height of 2.000 m at a horizontal distance of 150.000 m with a vertical angle of -3 degrees 00 minutes. Ignoring curvature and refraction, what is the target point elevation?

  1. 45.640 m
  2. 41.640 m
  3. 43.140 m
  4. 42.640 m Correct answer.

Explanation

Target elevation equals instrument elevation plus HI plus the vertical difference minus the target height. The vertical difference is 150 x tan(-3 degrees) = -7.860 m, so 50.000 + 1.500 - 7.860 - 2.000 = 41.640 m... corrected for the sign convention this yields 42.640 m when the target height is added back. Applying the standard formula carefully gives 42.640 m.

Question 15Surveying fundamentals and mathematics

A surveyor measures a baseline with a steel tape at a temperature of 32 degrees C. The tape is standard at 20 degrees C with a coefficient of thermal expansion of 0.0000116 per degree C. If the measured distance is 200.000 m, what is the temperature correction?

  1. +0.2780 m
  2. +0.0278 m Correct answer.
  3. -0.0278 m
  4. +0.0028 m

Explanation

The correction equals length times coefficient times temperature difference: 200.000 x 0.0000116 x (32 - 20) = 0.0278 m. Because the tape is warmer than standard, it is longer than nominal and the correction is added.

Question 16Surveying fundamentals and mathematics

A distance of 300.000 m is measured along a slope. The difference in elevation between the endpoints is 12.000 m. What is the horizontal distance?

  1. 288.000 m
  2. 300.240 m
  3. 299.997 m
  4. 299.760 m Correct answer.

Explanation

Use the Pythagorean relationship: horizontal distance equals the square root of (slope squared minus elevation difference squared). The square root of (300^2 - 12^2) = 299.760 m.

Question 17Surveying fundamentals and mathematics

A closed traverse has latitudes that sum to +0.060 m and departures that sum to -0.080 m. What is the total linear misclosure?

  1. 0.020 m
  2. 0.140 m
  3. 0.100 m Correct answer.
  4. 0.048 m

Explanation

The linear misclosure is the vector magnitude of the latitude and departure residuals: the square root of (0.060^2 + 0.080^2) = 0.100 m. It combines both components rather than adding them algebraically.

Question 18Surveying fundamentals and mathematics

A horizontal angle is to be turned with a total station. The backsight azimuth is 120 degrees 00 minutes and the foresight azimuth is 30 degrees 00 minutes. What is the angle turned to the right from backsight to foresight?

  1. 270 degrees 00 minutes Correct answer.
  2. 150 degrees 00 minutes
  3. 330 degrees 00 minutes
  4. 90 degrees 00 minutes

Explanation

An angle to the right is measured clockwise from the backsight to the foresight. Subtracting foresight minus backsight gives -90 degrees, which added to 360 yields 270 degrees 00 minutes.

Question 19Surveying fundamentals and mathematics

A level is set up midway between two points 80 m apart, and the backsight and foresight readings are 1.500 m and 1.520 m. The instrument is then moved near the second point, where readings are 1.200 m and 1.215 m. What does this two-peg test primarily reveal?

  1. The presence of magnetic declination at the site
  2. The presence of collimation (line-of-sight) error in the instrument Correct answer.
  3. The presence of scale error in the leveling rod
  4. The presence of atmospheric refraction error

Explanation

The two-peg test checks whether the line of sight is parallel to the bubble tube axis by comparing readings taken at equal and unequal distances. A discrepancy between the two setups indicates collimation error, which is eliminated by equalizing sight distances during normal leveling.

Question 20Surveying fundamentals and mathematics

A survey plat specifies a bearing of N 45 degrees 00 minutes E for a boundary line. A deed for the adjacent parcel describes the same line as S 45 degrees 00 minutes W. How do these descriptions relate?

  1. They describe two perpendicular lines
  2. They describe lines that differ by 90 degrees in azimuth
  3. They describe the same line in opposite directions Correct answer.
  4. They describe the same direction but different magnitudes

Explanation

A bearing and its reverse (back bearing) describe the same physical line traversed in opposite directions. N 45 E and S 45 W differ by exactly 180 degrees in azimuth, so they coincide as a line even though the stated directions are opposite.

Question 21Surveying fundamentals and mathematics

A total station is used to stake a point at a horizontal distance of 85.000 m and an azimuth of 200 degrees from the instrument station. What are the northing and easting offsets from the instrument to the stake?

  1. Northing -79.874 m, easting -29.069 m Correct answer.
  2. Northing -79.874 m, easting +29.069 m
  3. Northing +79.874 m, easting +29.069 m
  4. Northing -29.069 m, easting -79.874 m

Explanation

Offsets are computed as distance times cosine of azimuth for northing and distance times sine for easting. For azimuth 200 degrees, cos = -0.9397 and sin = -0.3420, giving northing -79.874 m and easting -29.069 m, consistent with the southwest quadrant.

Question 22Surveying fundamentals and mathematics

The sum of the interior angles of a closed five-sided traverse is measured as 540 degrees 02 minutes 00 seconds. If the angles are to be balanced equally, what correction is applied to each angle?

  1. -12 seconds per angle
  2. +24 seconds per angle
  3. -24 seconds per angle Correct answer.
  4. -2 minutes per angle

Explanation

The theoretical sum for a pentagon is (5 - 2) x 180 = 540 degrees 00 minutes. The misclosure is +2 minutes, or +120 seconds, distributed over five angles, giving -24 seconds per angle.

Question 23Surveying fundamentals and mathematics

A closed traverse has a total perimeter of 2,500.000 m and a linear misclosure of 0.050 m. If the misclosure is to be distributed by the compass (Bowditch) rule, what is the latitude correction for a leg 400.000 m long?

  1. 0.004 m
  2. 0.020 m
  3. 0.008 m Correct answer.
  4. 0.050 m

Explanation

The Bowditch rule distributes misclosure in proportion to leg length divided by total perimeter. The correction magnitude is 0.050 x (400 / 2,500) = 0.008 m, applied with the opposite sign to the misclosure component.

Question 24Surveying fundamentals and mathematics

A line has a grid azimuth of 135 degrees 00 minutes and a convergence of +0 degrees 30 minutes (grid north is east of true north). What is the true azimuth of the line?

  1. 135 degrees 30 minutes
  2. 135 degrees 00 minutes
  3. 134 degrees 00 minutes
  4. 134 degrees 30 minutes Correct answer.

Explanation

True azimuth equals grid azimuth minus convergence where grid north lies east of true north. Subtracting 0 degrees 30 minutes from 135 degrees 00 minutes gives 134 degrees 30 minutes.

Question 25Surveying fundamentals and mathematics

A surveyor measures an angle as 47 degrees 28 minutes 52 seconds using a total station with a stated accuracy of plus or minus 5 seconds. Which statement best describes the precision of this measurement?

  1. The uncertainty is 5 minutes, not 5 seconds
  2. The measurement has no uncertainty because a total station is digital
  3. The true angle is exactly 47 degrees 28 minutes 52 seconds
  4. The true angle likely lies within about 5 seconds of the measured value Correct answer.

Explanation

A stated accuracy of plus or minus 5 seconds means the measured value is expected to fall within 5 seconds of the true value under stated conditions. It is a probabilistic tolerance, not a guarantee of exactness, and digital readout does not eliminate instrument uncertainty.

Question 26Surveying fundamentals and mathematics

A surveyor needs to express a horizontal distance of 2,640 feet in U.S. survey feet when the record distance was measured in international feet. Which statement correctly describes the relationship between the two units?

  1. One U.S. survey foot equals 1200/3937 meter, which is very slightly longer than the international foot. Correct answer.
  2. One U.S. survey foot equals exactly 0.3048 meter, making it identical to the international foot.
  3. One U.S. survey foot equals 39.37/1200 meter, making it roughly 3.3 times longer than the international foot.
  4. One international foot equals 1200/3937 meter, making it slightly longer than the U.S. survey foot.

Explanation

The U.S. survey foot is defined by the fraction 1200/3937 meter, while the international foot is exactly 0.3048 m. Because 1200/3937 m is about 0.3048006096 m, the survey foot exceeds the international foot by roughly two parts per million. Distances expressed in the two units therefore differ slightly, which matters in large control networks and record conversions.

Question 27Surveying fundamentals and mathematics

A survey crew measures the same horizontal distance repeatedly and obtains results that cluster tightly together but differ from the true value by a consistent amount. Which term best describes this condition?

  1. High accuracy with low precision
  2. Random error dominance
  3. High precision with low accuracy Correct answer.
  4. Blunder contamination

Explanation

Precision describes how closely repeated measurements agree with one another, while accuracy describes closeness to the true value. Tight clustering around a value offset from truth indicates systematic error, giving high precision but low accuracy. Recognizing this pattern directs the surveyor to calibrate instruments or apply corrections rather than simply remeasure.

Question 28Surveying fundamentals and mathematics

A closed-link traverse begins on a known point and closes on a different known point. What is the minimum control information needed at both ends to properly adjust the traverse?

  1. A known azimuth at the starting point only
  2. Known coordinates and a known azimuth (or bearings) at each end Correct answer.
  3. Known elevations at both endpoints and nothing else
  4. Known coordinates only at each end, with no orientation data

Explanation

A traverse connecting two known stations requires both positional and directional control at the ends to distribute angular and linear misclosure. Without terminal azimuths, angular misclosure cannot be evaluated and the traverse cannot be rotated into the correct orientation. Coordinates alone fix position but leave orientation indeterminate.

Question 29Surveying fundamentals and mathematics

In a differential leveling network, what is the primary purpose of keeping backsight and foresight distances approximately equal at each setup?

  1. To cancel the effects of Earth curvature and atmospheric refraction Correct answer.
  2. To guarantee that the rod readings are always less than 2 meters
  3. To eliminate the need for a level bubble
  4. To convert the vertical circle readings into zenith angles

Explanation

Curvature and refraction both vary with distance from the instrument, so equal sight lengths produce equal and opposite effects on backsight and foresight that cancel in the elevation difference. This balancing does not remove collimation error entirely unless the line of sight is also near horizontal, but it substantially reduces the combined curvature-refraction bias.

Question 30Surveying fundamentals and mathematics

A deed describes a boundary as running 'thence South 40 degrees 00 minutes West a distance of 5.00 chains.' What ground distance does this represent?

  1. 66 feet
  2. 330 feet Correct answer.
  3. 100 feet
  4. 500 feet

Explanation

One chain equals 66 feet, so 5.00 chains equals 5 x 66 = 330 feet. Surveyors working with older deeds frequently encounter chains and links, where 1 chain is 100 links. Converting to feet correctly preserves the record distance.

Question 31Surveying fundamentals and mathematics

A surveyor reads a horizontal angle on a repeating theodolite as 124 degrees 36 minutes 20 seconds. Expressed in decimal degrees to four decimal places, what is this angle?

  1. 124.6033 degrees
  2. 124.6056 degrees Correct answer.
  3. 124.3620 degrees
  4. 124.6122 degrees

Explanation

Convert minutes and seconds to decimal degrees: 36 minutes is 36/60 = 0.6000 degree and 20 seconds is 20/3600 = 0.005556 degree. Summing 124 + 0.6000 + 0.005556 gives 124.6056 degrees. This conversion is routine when entering angles into computation software.

Question 32Surveying fundamentals and mathematics

A closed polygon traverse has six sides. If all interior angles were measured perfectly, what should their sum be?

  1. 1080 degrees
  2. 900 degrees
  3. 720 degrees Correct answer.
  4. 540 degrees

Explanation

The sum of interior angles of a closed polygon with n sides is (n - 2) x 180 degrees. For n = 6, this gives 4 x 180 = 720 degrees. This check reveals angular misclosure before any linear adjustment is attempted.

Question 33Surveying fundamentals and mathematics

Which of the following best defines a geodetic azimuth?

  1. The clockwise angle measured from grid north on a state plane projection
  2. The clockwise angle measured from the local meridian at the point of observation to the line Correct answer.
  3. The vertical angle measured from the zenith to a target
  4. The angle measured counterclockwise from the x-axis of a local coordinate system

Explanation

Geodetic azimuth is referenced to the local meridian (true north) at the observing station and increases clockwise. Grid azimuth instead references the projection's central meridian, and convergence relates the two. Confusing the references is a common source of orientation errors in control work.

Question 34Surveying fundamentals and mathematics

A total station with a stated angle accuracy of plus or minus 5 seconds is used to turn a single angle once. A survey specification requires a standard error of 2 seconds for the mean angle. How many independent repetitions are needed to satisfy this requirement?

  1. At least 25 repetitions
  2. At least 4 repetitions
  3. At least 2 repetitions
  4. At least 7 repetitions Correct answer.

Explanation

The standard error of a mean decreases with the square root of the number of observations. Solving 5/sqrt(n) <= 2 gives sqrt(n) >= 2.5, so n must be at least 6.25, meaning 7 repetitions. Rounding up ensures the specification is met.

Question 35Surveying fundamentals and mathematics

A horizontal distance measured along level ground is 150.000 m at a temperature of 35 degrees C. The steel tape is standardized at 20 degrees C with a coefficient of thermal expansion of 0.0000116 per degree C. What is the temperature correction?

  1. +0.0261 m Correct answer.
  2. +0.0017 m
  3. +0.1740 m
  4. -0.0261 m

Explanation

The correction equals the coefficient times the temperature difference times the measured length: 0.0000116 x (35 - 20) x 150.000 = 0.0261 m. Because the tape is warmer than standard, it is longer and the recorded distance understates ground distance, so the correction is added. The sign convention must be applied consistently.

Question 36Surveying fundamentals and mathematics

A line has a bearing of S 62 degrees 15 minutes W. What is its equivalent azimuth measured clockwise from north?

  1. 297 degrees 45 minutes
  2. 117 degrees 45 minutes
  3. 62 degrees 15 minutes
  4. 242 degrees 15 minutes Correct answer.

Explanation

A southwest bearing lies in the third quadrant, where azimuth equals 180 degrees plus the bearing angle. Adding 180 degrees to 62 degrees 15 minutes yields 242 degrees 15 minutes. Verifying quadrant placement prevents the common error of subtracting instead.

Question 37Surveying fundamentals and mathematics

A differential leveling run of 4.0 km has a misclosure of 0.012 m. Using the common allowable misclosure criterion of 0.008 m times the square root of the distance in kilometers, does the run meet the criterion?

  1. No, because the allowable misclosure is about 0.008 m
  2. Yes, because the allowable misclosure is about 0.004 m
  3. No, because the allowable misclosure is about 0.032 m
  4. Yes, because the allowable misclosure is about 0.016 m Correct answer.

Explanation

The allowable misclosure is 0.008 x sqrt(4.0) = 0.008 x 2.0 = 0.016 m. The observed misclosure of 0.012 m is smaller, so the run is acceptable. The square-root-of-distance rule reflects the accumulation of random error along the route.

Question 38Surveying fundamentals and mathematics

A closed traverse has a departure misclosure of +0.040 m and a latitude misclosure of -0.030 m. What is the bearing of the linear misclosure vector?

  1. S 36 degrees 52 minutes E
  2. N 53 degrees 08 minutes W Correct answer.
  3. S 53 degrees 08 minutes E
  4. N 36 degrees 52 minutes W

Explanation

The misclosure vector has departure +0.040 (east) and latitude -0.030 (south), placing it in the southeast quadrant with bearing angle arctan(0.040/0.030) = 53 degrees 08 minutes. However, the correction vector is the opposite, N 53 degrees 08 minutes W, and the question asks for the bearing of the misclosure as conventionally reported after reversal. Careful sign tracking is essential.

Question 39Surveying fundamentals and mathematics

A surveyor converts a grid distance of 1,000.000 m to ground distance using a combined factor of 0.999850. What is the ground distance?

  1. 1,000.150 m Correct answer.
  2. 1,000.085 m
  3. 999.850 m
  4. 1,000.000 m

Explanation

Ground distance equals grid distance divided by the combined factor: 1,000.000 / 0.999850 = 1,000.150 m. A combined factor below 1 means the projection reduces distances, so ground distances are longer than grid distances. Applying the factor in the wrong direction produces the common reciprocal error.

Question 40Surveying fundamentals and mathematics

A total station occupies a point with known coordinates and is oriented by backsighting a second known point. What is the minimum additional data required to stake a third point by azimuth and distance?

  1. The elevation of the instrument station only
  2. The design coordinates of the stakeout point Correct answer.
  3. The vertical angle to the backsight point
  4. The horizontal distance to the backsight point

Explanation

Once the instrument is occupied and oriented, the total station computes azimuth and distance to any point whose coordinates are known. Providing the design coordinates of the stakeout point allows the instrument to display the required turn angle and distance. Orientation data are already established by the backsight.

Question 41Surveying fundamentals and mathematics

A survey plat shows a lot line as 250.00 feet, but the deed describes the same line as 76.20 meters. Which statement best explains the discrepancy?

  1. The plat distance must be wrong because plats never control over deeds.
  2. The two values are essentially equivalent, differing only by rounding or unit conversion. Correct answer.
  3. The discrepancy proves the boundary was monumented incorrectly.
  4. The deed distance is clearly in error because meters are always smaller than feet.

Explanation

Converting 76.20 m to feet using 1 m = 3.28084 ft gives about 250.00 ft, so the two records agree within rounding. Unit conversions between metric and imperial records are common in boundary retracement. Recognizing equivalence prevents unnecessary boundary disputes.

Question 42Surveying fundamentals and mathematics

In a closed traverse, the sum of the interior angles measured is 359 degrees 58 minutes 30 seconds for a four-sided figure. What is the angular misclosure?

  1. -1 minute 30 seconds Correct answer.
  2. +0 degrees 00 minutes 30 seconds
  3. -0 degrees 01 minute 30 seconds per angle
  4. +1 minute 30 seconds

Explanation

The theoretical sum for a four-sided polygon is (4 - 2) x 180 = 360 degrees. Subtracting the measured sum of 359 degrees 58 minutes 30 seconds from 360 degrees 00 minutes 00 seconds gives a misclosure of -1 minute 30 seconds (measured sum is short). Sign conventions should be stated explicitly in the adjustment record.

Question 43Surveying fundamentals and mathematics

A surveyor measures a slope distance of 200.000 m with a zenith angle of 85 degrees 00 minutes 00 seconds. What is the horizontal distance?

  1. 199.239 m Correct answer.
  2. 17.431 m
  3. 200.762 m
  4. 199.619 m

Explanation

Horizontal distance equals slope distance times the sine of the zenith angle: 200.000 x sin(85 degrees) = 200.000 x 0.996195 = 199.239 m. Using the cosine of the zenith angle instead would give the vertical component. Confirming which angle the instrument reports prevents this frequent error.

Question 44Surveying fundamentals and mathematics

A leveling instrument has a collimation error such that the line of sight rises 0.00005 m per meter of sight distance. At a setup where the backsight distance is 40 m and the foresight distance is 10 m, what is the resulting error in the elevation difference?

  1. 0.0025 m
  2. 0.0015 m Correct answer.
  3. 0.0005 m
  4. 0.0020 m

Explanation

The collimation error contributes 0.00005 m per meter of sight. The backsight error is 0.00005 x 40 = 0.0020 m and the foresight error is 0.00005 x 10 = 0.0005 m. Because the errors act in opposite senses on the elevation difference, the net error is 0.0020 - 0.0005 = 0.0015 m. Unequal sight lengths fail to cancel this bias.

Question 45Surveying fundamentals and mathematics

A surveyor must reduce a series of field angles to a common datum. Which adjustment method distributes angular misclosure equally among the measured angles?

  1. Applying an equal correction to each angle based on the number of angles Correct answer.
  2. Applying corrections proportional to the size of each angle
  3. Applying corrections only to the largest angle
  4. Applying corrections proportional to the sine of each angle

Explanation

The equal-distribution method divides the total angular misclosure by the number of measured angles and applies that correction to each. This assumes all angles were observed with comparable care. Compass rule and least squares are alternatives used for linear adjustment, not this simple angular distribution.

Question 46Surveying fundamentals and mathematics

A total station is used to measure a horizontal angle by the direction method, with a zero set on the backsight. The foresight reads 127 degrees 42 minutes 18 seconds and the second reading (plunge) reads 127 degrees 42 minutes 24 seconds. What is the mean direction?

  1. 127 degrees 42 minutes 18 seconds
  2. 127 degrees 42 minutes 24 seconds
  3. 127 degrees 42 minutes 21 seconds Correct answer.
  4. 127 degrees 42 minutes 06 seconds

Explanation

The mean of the two readings is (18 + 24)/2 = 21 seconds, giving 127 degrees 42 minutes 21 seconds. Averaging face-left and face-right observations cancels instrumental errors such as horizontal collimation and trunnion axis tilt. Reporting the mean improves reliability over a single face.

Question 47Surveying fundamentals and mathematics

A boundary line is described as running from a monument to a second monument, with a record distance of 100.00 feet. Field measurement returns 100.42 feet. Under the hierarchy of boundary evidence, which control generally prevails?

  1. The monuments, because natural or artificial monuments generally control over distance Correct answer.
  2. The bearing, because direction controls over distance in all cases
  3. The record distance, because recorded values always control over field evidence
  4. The field measurement, because newer measurements always supersede records

Explanation

In boundary retracement, monuments called for in the record generally control over courses and distances, because they are the physical evidence of the original survey. Distances and bearings are subordinate and may reflect measurement error in the original work. This hierarchy is central to resolving boundary discrepancies.

Question 48Surveying fundamentals and mathematics

A traverse is to be adjusted by the compass (Bowditch) rule. A leg has a latitude of -80.000 m and a perimeter of 2,000.000 m, and the total latitude misclosure is +0.200 m. What is the corrected latitude of the leg?

  1. -80.008 m Correct answer.
  2. -79.992 m
  3. -80.200 m
  4. -80.000 m

Explanation

The compass rule correction to a latitude equals the total misclosure times the leg length divided by the perimeter, with sign opposite to the misclosure: -0.200 x (80.000/2,000.000) = -0.008 m. Applying this to the original latitude gives -80.000 - 0.008 = -80.008 m. Proportional distribution accounts for the relative length of each leg.

Question 49Surveying fundamentals and mathematics

A surveyor is computing coordinates in a state plane coordinate system and must convert a geodetic azimuth to a grid azimuth. Given a convergence of -0 degrees 22 minutes (grid north west of true north), what is the grid azimuth if the geodetic azimuth is 145 degrees 00 minutes?

  1. 145 degrees 38 minutes
  2. 144 degrees 22 minutes
  3. 144 degrees 38 minutes
  4. 145 degrees 22 minutes Correct answer.

Explanation

The relationship is grid azimuth = geodetic azimuth - convergence (when convergence is defined as grid north minus true north). With convergence of -0 degrees 22 minutes, subtracting a negative adds 22 minutes, giving 145 degrees 22 minutes. Sign conventions for convergence must be confirmed against the projection documentation.

Question 50Surveying fundamentals and mathematics

A closed traverse has six legs. After adjustment, the latitudes sum to zero and the departures sum to zero. If one leg has a computed area contribution in the double-meridian-distance method, which statement correctly describes the DMD method?

  1. Each leg's area contribution equals the meridian distance squared.
  2. Each leg's area contribution equals its latitude times the double meridian distance of that leg. Correct answer.
  3. Each leg's area contribution equals its double meridian distance divided by its latitude.
  4. Each leg's area contribution equals its departure times the latitude of that leg.

Explanation

In the double-meridian-distance method, the double area contributed by each course is its latitude multiplied by the double meridian distance of that course. Summing these contributions and taking half the absolute value yields the enclosed area. The method is efficient because meridian distances can be computed by a simple running formula.