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Distance and Bearing Between Two Points

Mediumcoordinatesbearing
Point A is at E = 500 m, N = 1000 m and point B is at E = 800 m, N = 1400 m. The distance and bearing from A to B are:
  1. A500 m, N53.1°E
  2. B700 m, N36.9°E
  3. C500 m, S36.9°E
  4. D500 m, N36.9°E
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Answer: D. 500 m, N36.9°E

Equations: distance L = √(ΔE² + ΔN²). Bearing angle from north, θ = tan⁻¹(|ΔE| / |ΔN|); the signs of ΔN and ΔE give the quadrant. Values: ΔE = EB − EA = 800 − 500 = +300 m. ΔN = NB − NA = 1400 − 1000 = +400 m. Step 1: L = √(300² + 400²) = √250,000 = 500 m. Step 2: θ = tan⁻¹(300/400) = 36.9°. Step 3: ΔN is positive (north) and ΔE is positive (east), so the bearing is N36.9°E. tan⁻¹(400/300) = 53.1° measures from east instead of north, and 700 m adds ΔE and ΔN instead of using Pythagoras.
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