The Math Meridian
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Trigonometry in 3D and with bearings

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Useful for: MCR3U MBF3C IB Math AA SL & HL IB Math AI SL & HL

Learn it Bearings are measured clockwise from north (e.g. 120°). Sketch the situation, find the angle inside the triangle, then use the sine or cosine law. In 3D problems, find a right triangle in a plane first, then use it in a second triangle.

Example: A ship sails 30 km on bearing 040°, then 20 km on bearing 130°. How far is it from the start?

  1. The turn makes a 90° angle between the two legs.
  2. d = √(30² + 20²) ≈ 36.1 km.

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