Ending Coordinates from Azimuth
Mediumcoordinatestraverse
A survey line starts at E = 2000 m, N = 3000 m, is 250 m long, and has an azimuth of 120°. The ending coordinates are most nearly:
- AE = 2125, N = 3217
- BE = 1875, N = 3217
- CE = 2217, N = 2875
- DE = 1783, N = 2875
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Answer: C. E = 2217, N = 2875
Equations: departure ΔE = L·sin(Az) and latitude ΔN = L·cos(Az), where Az is measured clockwise from north. Values: L = 250 m is the line length. Az = 120° is the azimuth, measured clockwise from the north arrow. The start point is E = 2000 m, N = 3000 m. Step 1: ΔE = 250 × sin120° = 250 × 0.866 = +216.5 m (east). Step 2: ΔN = 250 × cos120° = 250 × (−0.5) = −125 m (south). Step 3: E = 2000 + 216.5 = 2216.5 m and N = 3000 − 125 = 2875 m. Swapping sin and cos gives E = 1875, N = 3217, which is the classic error of measuring the azimuth from east.
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