Trigonometry with Bearings

Trigonometry with Bearings Revision Content

Understanding Bearings

  • Bearings are used in navigation to define the direction of one point relative to another. They are measured in degrees from the North line in a clockwise direction, typically expressed as a three-figure bearing.
  • Always remember that bearing measurements should be between 0 and 360 degrees.

Basic Principles

  • When reading or writing bearings, remember that a bearing must be a three-figure measurement. For example, “60°” would be written as “060°”.
  • Be aware that bearings are always measured clockwise.

Calculating Bearings in Trig Problems

  • To find the bearing, you can use basic geometry (usually involving right-angled triangles) and trigonometry. The cosine rule, sine rule or Pythagoras’ theorem might also be used, depending on the problem.
  • Remember that sine, cosine, and tangent apply to right-angled triangles - sin = opposite/hypotenuse, cos = adjacent/hypotenuse, and tan = opposite/adjacent.
  • You may also use these equations backwards to find angles, using the inverse functions sin^(-1), cos^(-1), and tan^(-1).

Applied Examples

  • The angle of depression or elevation can be calculated using trigonometry when working with bearings and height problems.
  • When asked to calculate a bearing, always remember to give your answer as a three figure bearing (claim to the nearest degree).