RPLS Mathematics and Geodesy 3

Question 1

In State Plane Coordinate (SPC) systems, which projection is used for zones that are taller (north-south) than they are wide?

Accepted Answer

Transverse Mercator

Answer

Transverse Mercator projection is used for SPC zones elongated in the north-south direction, such as those in narrow states.

Question 2

What is the arc length (s) of a simple circular curve given a radius of 500 ft and a central angle (Δ) of 30°?

Accepted Answer

261.80 ft

Answer

s = R × Δ(radians) = 500 × (30 × π/180) = 500 × 0.5236 = 261.80 ft.

Question 3

A level rod reading taken with an automatic level is 4.872 ft. The HI is 105.234 ft. What is the elevation of the rod point?

Accepted Answer

100.362 ft

Answer

Elevation = HI − rod reading = 105.234 − 4.872 = 100.362 ft.

Question 4

Which type of error is introduced when a surveyor consistently reads a micrometer one division too high on every observation?

Accepted Answer

Systematic error

Answer

Systematic errors follow a predictable pattern and cannot be removed by averaging; they require calibration or correction procedures.

Question 5

In a geodetic context, the 'prime vertical' is the plane that passes through an observer and is oriented in which direction?

Accepted Answer

East-west through the zenith and nadir

Answer

The prime vertical is the vertical plane through the observer oriented east-west, perpendicular to the meridian plane.

(RPLS) Registered Professional Land Surveyor Practice Test