From ancient Polynesian wayfinders to modern GPS systems, trigonometry has been the cornerstone of navigation technology.
Celestial Navigation
- Sextant Measurements: Angle between horizon and celestial body
- Latitude Determination: Using Polaris altitude (Northern Hemisphere)
- Longitude Calculation: Lunar distance method with timekeeping
Latitude = 90° - observed altitude + declination
Modern GPS Technology
Global Positioning Systems use trilateration:
- Measure distances to 4+ satellites
- Solve spherical trigonometry equations
- Account for relativistic time corrections
Distance Calculation
Ship spots lighthouse 15° above horizon. Lighthouse height = 50m.
Distance = height / tan(angle)
= 50 / tan(15°) ≈ 186.6m
Aviation Applications
- Great circle routes (shortest path between points on globe)
- VOR (VHF Omnidirectional Range) navigation
- Wind correction angle calculations