To find angle ABC from the bearings of B from A and C from B, reverse the first bearing. Angle ABC is measured at B, so both rays must start there. Compare the bearing of A from B with the bearing of C from B.
The 2027 SEC G3 Mathematics K310 syllabus includes bearings in trigonometry problems. This guide shows how to find the angle inside a triangle and how to handle bearings on opposite sides of north.
- Mark the vertex named in the middle.
- Draw a north line through that vertex.
- Reverse any bearing that points towards it.
- Use the smaller turn for the interior angle.
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Read the bearing from its starting point
“The bearing of B from A” starts at A. Its reverse starts at B and points towards A. Add 180° and subtract 360° if needed to bring the result into the range from 000° to 359° for whole-degree bearings.
An interior angle compares two rays that start at the same point. Draw both bearings from B using the same north line so their difference has a geometric meaning.
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Worked example | A change of direction at B
A boat sails from A to B on a bearing of 060°, then from B to C on a bearing of 150°. At B, the ray back towards A has bearing 060° + 180° = 240°. The ray towards C has bearing 150°. Angle ABC is 240° − 150° = 90°.
The change from the boat’s incoming heading to its outgoing heading happens to be 90° in this example too. To see the difference, change the outgoing bearing to 120°. The boat turns through 60°, but angle ABC is 240° − 120° = 120°. The interior angle uses the ray back towards A.
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Compare bearings that straddle north
Suppose the bearings from B towards A and C are 340° and 030°. The numerical difference is 310°. The smaller turn goes 20° to north and 30° beyond north, giving an interior angle of 50°. You can also calculate 360° − 310°.
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Frequently asked questions
Do I write the interior angle with three digits?
Use three figures for a whole-degree bearing, such as 060°. An ordinary interior angle can be written as 60°.
How can a parent check the setup?
Ask the student to place a finger at B and trace each ray outwards. Both arrows used to find angle ABC should leave B.