COGO Forward Locate (Bearing and Distance)
The single COGO step traverse-closure only ever sums over a loop: from a known point, an azimuth (clockwise from north), and a distance, the new coordinates. Latitude dN = D cos(Az), departure dE = D sin(Az); N2 = N1 + dN, E2 = E1 + dE. From N5000/E5000 at azimuth 45 deg over 200 ft the point lands N5141.42/E5141.42. Convert a quadrant bearing (N45E) to azimuth first (bearing-conversion). Plane geometry - no curvature or grid scale factor; the project control and datum govern.
Formula and source
latitude (delta N) = D cos(Az); departure (delta E) = D sin(Az); N2 = N1 + delta N; E2 = E1 + delta E. Az is the azimuth clockwise from north.
First-principles coordinate geometry (latitude / departure) as compiled in the standard route-surveying references (Ghilani & Wolf, Elementary Surveying; FM 5-233), by name.
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