Trigonometry is used in land surveying to calculate distances and angles between points based on measurements and angles taken in the field. For example, the tangent, sine, and cosine functions help in determining unknown distances or angles when the surveyor has partial measurements.
To determine the new coordinates (X2, Y2), you use trigonometric functions where X2 is calculated using the cosine of the angle and Y2 is calculated using the sine of the angle. For a distance of 100 meters and an angle of 30 degrees, this translates to X2 = X1 + 100 * cos(30°) and Y2 = Y1 + 100 * sin(30°).
The State Plane Coordinate System (SPCS) is used to provide a local coordinate system that is specific to a region or state. It is designed to reduce distortion in mapping and surveying by using projections that fit the local area, making it easier to work with accurate coordinates.
Converting between different coordinate systems often requires applying specific transformation equations and parameters to account for differences in projection, datum, and scale. This ensures that coordinates are accurately converted from one system to another.
The "error of closure" refers to the discrepancy that occurs when comparing the starting and ending points in a closed traverse survey. This error indicates the accuracy of the measurements taken and helps to identify any discrepancies that need to be corrected for precise survey results.
