Calculations - Practical Boundary Surveying - page 202

Fig. 14.1 Angles and distances converted to coordinates
with negative numbers, but it is easier just to pick relatively large numbers such as
N5,000, E5,000 so we don't have to deal with minus signs.
We will assign Point 1 the starting value of N5,000, E5,000. During our field
work, the line from 1 to 2 was sighted with a magnetic compass. The magnetic
bearing was N45°E. By starting at Point 1 and going N45°E, 141.42 feet, and
using a little trigonometry, we can calculate the coordinates of Point 2 (N5,100,
E5,100). Recall that a bearing in the NE quadrant is simply an angle measured
from north in an easterly direction. So our bearing N45°E is simply an angle
which is 45° to the right of north.
Because we know the bearing of line 1-2 and the angle to point 3 (104° 08′
14″), we can calculate the bearing of the line 2-3. The appendix has examples
of calculating bearings using angles. Using this bearing and the distance of
121.63 feet we can calculate the coordinates of point 3.
With this method, we can calculate the bearings of each of the lines and the
coordinates for each of the points, as shown in Fig. 14.2 . This may seem like a
lot of effort, but our computer will do most of the work for us. In fact, software is