Question

Given the following plane rectangular coordinates for traverse station 3 and 4, compute the distance and azimuth of the line from 3 to 4. Station X, m Y, m 3 525,549.045 148,098.104 4 524,042.132 148,518.135

Answer 1

The distance between traverse station 3 and 4 is approximately 148.3 meters, with an azimuth of 89.1 degrees.

Explanation:

To determine the distance and azimuth between traverse station 3 and 4, we employ the coordinates provided. Using the plane rectangular coordinates (X, Y), we calculate the difference in X and Y coordinates for stations 3 and 4. Subsequently, utilizing these differences, we apply the distance formula to obtain the straight-line distance between the two stations. This calculation yields a distance of approximately 148.3 meters.

For the azimuth, we compute the angle of the line by implementing the arctangent function of the difference in Y coordinates divided by the difference in X coordinates. This computation gives us an azimuth of roughly 89.1 degrees.

By utilizing basic coordinate geometry principles, specifically the distance formula and trigonometric functions, we determine the distance and azimuth between the given traverse stations. These calculations rely on the differences in X and Y coordinates, providing an accurate measure of the straight-line distance and directional angle between the two points.