Mathematics and Geomatics Flashcards

A horizontal curve has a radius of 1,200 ft and a central angle (Δ) of 24°30'. The tangent length T equals:

Answer: 261.5 ft

T = R × tan(Δ/2) = 1200 × tan(12°15') = 1200 × 0.2174 ≈ 261.5 ft.

The relationship between geodetic height (h), orthometric height (H), and geoid undulation (N) is:

Answer: h = H + N

Geodetic (ellipsoidal) height h equals orthometric height H plus geoid undulation N: h = H + N.

A closed traverse has 5 sides. The sum of interior angles should equal:

Answer: 540°

Sum of interior angles = (n - 2) × 180° = (5 - 2) × 180° = 540°.

In coordinate geometry (COGO), the inverse computation determines:

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.

The scale factor in a State Plane Coordinate System (SPCS) is applied to account for:

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.

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:

Answer: 485.51 ft

HD = SD × cos(vertical angle) = 487.34 × cos(5°22') = 487.34 × 0.9956 ≈ 485.51 ft.

In photogrammetry, the principal distance (c) of a camera is most accurately defined as:

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.