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).