LSIT Mathematics and Geomatics 3 — Questions and Answers
Question 1: A horizontal curve has a radius of 1,200 ft and a central angle (Δ) of 24°30'. The tangent length T equals:
- 261.5 ft (Correct answer)
- 512.4 ft
- 523.0 ft
- 130.8 ft
Correct answer: 261.5 ft
T = R × tan(Δ/2) = 1200 × tan(12°15') = 1200 × 0.2174 ≈ 261.5 ft.
Question 2: The relationship between geodetic height (h), orthometric height (H), and geoid undulation (N) is:
- h = H + N (Correct answer)
- H = h + N
- N = h + H
- h = H × N
Correct answer: h = H + N
Geodetic (ellipsoidal) height h equals orthometric height H plus geoid undulation N: h = H + N.
Question 3: A closed traverse has 5 sides. The sum of interior angles should equal:
- 540° (Correct answer)
- 360°
- 720°
- 900°
Correct answer: 540°
Sum of interior angles = (n - 2) × 180° = (5 - 2) × 180° = 540°.
Question 4: In coordinate geometry (COGO), the inverse computation determines:
- Distance and bearing between two known coordinate pairs (Correct answer)
- Unknown coordinates from a known point using bearing and distance
- Intersection of two bearing lines
- Area of a polygon from coordinates
Correct answer: Distance and bearing between two known coordinate pairs
The inverse problem computes direction (bearing/azimuth) and distance from the coordinates of two known points.
Question 5: The scale factor in a State Plane Coordinate System (SPCS) is applied to account for:
- The difference between grid distances on the projection plane and geodetic distances on the ellipsoid (Correct answer)
- Elevation differences between survey stations
- Magnetic declination corrections
- Temperature effects on steel tapes
Correct answer: The difference between grid distances on the projection plane and geodetic distances on the ellipsoid
The grid scale factor converts ellipsoidal geodetic distances to grid (plane) distances used in SPCS computations.
Question 6: A surveyor uses a total station that measures slope distance as 487.34 ft at a vertical angle of +5°22'. The horizontal distance is approximately:
- 485.51 ft (Correct answer)
- 489.18 ft
- 487.34 ft
- 483.67 ft
Correct answer: 485.51 ft
HD = SD × cos(vertical angle) = 487.34 × cos(5°22') = 487.34 × 0.9956 ≈ 485.51 ft.
Question 7: In photogrammetry, the principal distance (c) of a camera is most accurately defined as:
- The perpendicular distance from the rear nodal point of the lens to the image plane (Correct answer)
- The focal length printed on the camera body
- The distance from the camera to the ground
- The baseline distance between two exposure stations
Correct answer: The perpendicular distance from the rear nodal point of the lens to the image plane
Principal distance (calibrated focal length) is the distance from the rear nodal point to the principal point on the image plane, determined by calibration.
LSIT Mathematics and Geomatics 3
A horizontal curve has a radius of 1,200 ft and a central angle (Δ) of 24°30'.
The tangent length T equals: