AI generatedGeometry and measuresGCSE Higher

Bearings using non-right-angled trigonometry

Bearings using non-right-angled trigonometry.

  • Label the sides and angles before choosing a rule.
  • Sine rule: matching opposite pairs. Cosine rule: three sides or two sides and the included angle.
  • Use degree mode. Keep full calculator accuracy until the final rounding step.

Example 1

A boat travels 8 km from A to B on a bearing of 040°, then 6 km from B to C on a bearing of 100°. Find AC to 1 decimal place.

Two-leg route with north linesNNABC8 km6 kmDiagram not to scale
Bearing of A from BReverse the first bearing.
Find the angle between BA and BC.Use the cosine rule for the direct distance.Take the root and round at the end.

Example 2

A boat travels 9 km from A to B on a bearing of 041°, then 6 km from B to C on a bearing of 101°. Find AC to 1 decimal place.

Two-leg route with north linesNNABC9 km6 kmDiagram not to scale
Bearing of A from BReverse the first bearing.
Find the angle between BA and BC.Use the cosine rule for the direct distance.Take the root and round at the end.

Your turn

Question 1

A boat travels 10 km from A to B on a bearing of 042°, then 6 km from B to C on a bearing of 102°. Find AC to 1 decimal place.

Two-leg route with north linesNNABC10 km6 kmDiagram not to scale
Check answer
Bearing of A from BReverse the first bearing.
Find the angle between BA and BC.Use the cosine rule for the direct distance.Take the root and round at the end.
Question 2

A boat travels 11 km from A to B on a bearing of 043°, then 6 km from B to C on a bearing of 103°. Find AC to 1 decimal place.

Two-leg route with north linesNNABC11 km6 kmDiagram not to scale
Check answer
Bearing of A from BReverse the first bearing.
Find the angle between BA and BC.Use the cosine rule for the direct distance.Take the root and round at the end.
Question 3

A boat travels 12 km from A to B on a bearing of 044°, then 6 km from B to C on a bearing of 104°. Find AC to 1 decimal place.

Two-leg route with north linesNNABC12 km6 kmDiagram not to scale
Check answer
Bearing of A from BReverse the first bearing.
Find the angle between BA and BC.Use the cosine rule for the direct distance.Take the root and round at the end.
Question 4

A boat travels 13 km from A to B on a bearing of 045°, then 6 km from B to C on a bearing of 105°. Find AC to 1 decimal place.

Two-leg route with north linesNNABC13 km6 kmDiagram not to scale
Check answer
Bearing of A from BReverse the first bearing.
Find the angle between BA and BC.Use the cosine rule for the direct distance.Take the root and round at the end.
Question 5

A boat travels 14 km from A to B on a bearing of 046°, then 6 km from B to C on a bearing of 106°. Find AC to 1 decimal place.

Two-leg route with north linesNNABC14 km6 kmDiagram not to scale
Check answer
Bearing of A from BReverse the first bearing.
Find the angle between BA and BC.Use the cosine rule for the direct distance.Take the root and round at the end.
← All Geometry and measures cardsReport a mistake