Trigo Bearings
In this lesson, you will learn how to solve problems involving bearings in trigonometry. Bearings are measured in degrees from the north direction, moving clockwise, and are always written as three-digit angles. You will learn how to interpret diagrams correctly, identify the given angles, and determine the bearings.
Related Lessons:
How To Find The Bearings
Key rules when finding the bearings:
- Must be measure from the North
- Measure in a clockwise direction
- Must be in 3-digit format, e.g. 001°, 041°, 300°
- Angles in 1 decimal place, if required e.g 001.2°, 041.1°, 300.9°
One of the biggest challenges students face in bearings is interpreting the question correctly. If you are asked to find the “Bearing of B from A,” it means you start from point A, face north, and then measure clockwise until you reach the line connecting A to B. That is the angle that you need to find.
Example 1
A, B and C are three points on level ground and AC=BC. B is on a bearing of 050o from A. C is on a bearing of 105° from A. Find
- angle ABC
- the bearing of C from B
- the bearing of A from C
Example 2
Port A is due North of another Port B. A cruise ship sets sail from Port B on a straight course with a bearing 050° to Port D until it passes a point C where it is the shortest distance from Port A. The distance BC is 3.6 km. The cruise ship finally reaches Port D. Calculate
- the bearing of C from A.
- the bearing of A from C.
- the distance AB.
- If the distance from Port B to Port D is 10km, find the area of ΔABD.
Example 3
A, B and C are three points on level ground and AC=BC. B is on a bearing of 075° from A . C is on a bearing of 114° from A. Find
- angle ABC
- the bearing of C from B
- the bearing of A from C
Example 4
The diagram shows the positions of three towns, A, B and C, such that A is equidistant from B and C. B is due east of A and angle ABC=75°. Find
- the reflex angle ACB
- the bearing of C from A