LSIT Mathematics and Geomatics 1 — Questions and Answers
Question 1: What is the primary purpose of using trigonometry in land surveying?
- To calculate the cost of construction materials
- To determine distances and angles between points (Correct answer)
- To measure soil composition
- To analyze the weather conditions
Correct answer: To determine distances and angles between points
Trigonometry is fundamental to land surveying because it provides the mathematical tools to calculate unknown distances, angles, and elevations from known measurements. Surveyors use trigonometric functions (sine, cosine, tangent) to solve triangles formed by survey points, allowing them to precisely determine the relative positions of features on the Earth's surface. This is essential for mapping, boundary determination, and construction layout.
Question 2: How is the "State Plane Coordinate System" used in land surveying?
- To determine the elevation of a land parcel
- To provide a local coordinate system for accurate mapping and surveying (Correct answer)
- To calculate the volume of materials for construction
- To measure horizontal angles between survey points
Correct answer: To provide a local coordinate system for accurate mapping and surveying
The State Plane Coordinate System (SPCS) is a set of geographic coordinate systems established by the National Geodetic Survey for each U.S. state. Its primary purpose in land surveying is to provide a consistent, high-accuracy, two-dimensional (northing and easting) coordinate system that minimizes distortion over smaller areas. This allows surveyors to perform precise measurements and mapping within a specific state, linking local surveys to a national geodetic framework.
Question 3: If a surveyor has a known coordinate point (X1, Y1) and measures an angle of 30 degrees and a distance of 100 meters from this point, what is the coordinate of the new point (X2, Y2) assuming no elevation change?
- X2 = X1 + 100 * cos(30°), Y2 = Y1 + 100 * sin(30°) (Correct answer)
- X2 = X1 + 100 * tan(30°), Y2 = Y1 + 100 * cos(30°)
- X2 = X1 - 100 * cos(30°), Y2 = Y1 - 100 * sin(30°)
- X2 = X1 + 100 * sin(30°), Y2 = Y1 + 100 * cos(30°)
Correct answer: X2 = X1 + 100 * cos(30°), Y2 = Y1 + 100 * sin(30°)
This formula applies basic trigonometry to calculate new coordinates from a known point, distance, and bearing (angle). In a Cartesian coordinate system, the change in the X-coordinate (easting) is found by multiplying the distance by the cosine of the angle, and the change in the Y-coordinate (northing) is found by multiplying the distance by the sine of the angle. Assuming the angle is measured from the positive X-axis counter-clockwise, this formula correctly projects the new point.
Question 4: Which of the following is a common method for converting between different coordinate systems?
- Using a clinometer
- Applying transformation equations and parameters (Correct answer)
- Measuring angles with a theodolite
- Using a GPS receiver
Correct answer: Applying transformation equations and parameters
Converting between different coordinate systems (e.g., from a local grid to a state plane system, or between different datums) requires the use of specific mathematical transformation equations. These equations incorporate parameters that account for differences in origin, orientation, scale, and datum between the systems. Surveyors use these precise transformations to accurately translate coordinates from one system to another, ensuring consistency and compatibility of spatial data.
Question 5: In surveying, what does the term "error of closure" refer to?
- The difference between the measured and actual elevation of a point
- The discrepancy between the starting and ending point in a closed traverse survey (Correct answer)
- The error in the measurement of angles due to instrument calibration
- The difference between the recorded and actual coordinates of a survey point
Correct answer: The discrepancy between the starting and ending point in a closed traverse survey
In a closed traverse survey, a surveyor measures angles and distances around a polygon that begins and ends at the same known point. Theoretically, the sum of the measured angles and distances should bring the surveyor back exactly to the starting point. The 'error of closure' is the small, unavoidable discrepancy between the calculated coordinates of the starting point and the ending point, indicating the overall accuracy of the survey measurements.
LSIT Mathematics and Geomatics 1
What is the primary purpose of using trigonometry in land surveying?