📘 Remember
- Label the triangle before choosing a formula.
- Use degree mode unless the question says otherwise.
- Keep full calculator values until the final rounding step.
🎯 Learning Objectives
- draw three-figure bearing diagrams;
- form right triangles from navigation information;
- use north lines consistently;
- calculate distances and angles in bearing problems.
Introduction
This lesson develops Bearings with Trigonometry from meaning and patterns before moving to calculations. Look for what the quantities, shapes or symbols represent, then connect that idea to the method.
Key Notes
Read the definitions and key facts below carefully. Each rule is most useful when you can explain why it fits the situation, not simply recall it.
Setting Up the Diagram
Worked Example
A boat travels 12 km on a bearing of 060°. Its eastward component is opposite the 60° angle.
Eastward distance=12sin60°≈10.4 km.
Northward distance=12cos60°=6 km.
Practice Questions
- A plane travels 20 km on bearing 030°. Find its northward component.
- For the same journey, find its eastward component.
- Why must a north line be drawn at each relevant point?
- Find the reverse bearing of 075°.
✅ Check Your Work
Show answers and working
- 20cos30°≈17.3 km.
- 20sin30°=10 km.
- Bearings are measured from north at the point where the bearing begins.
- 255°.
🧭 Interactive Lab: Interactive Bearing Compass
Change the values or make a choice and watch the mathematics respond.
Summary
⚠️ Common Mistakes
- Using the wrong reference angle.
- Rounding too early.
- Forgetting units or the degree symbol.
⭐ Exam Tips
- Write the formula before substituting.
- Sketch and label any diagram that is not already provided.
- Check whether the answer is sensible for the shape.
🌍 Did You Know?
Surveyors, engineers, pilots and architects use trigonometry to calculate distances that are difficult or unsafe to measure directly.
Common Mistakes
- Choosing a rule before identifying what the question describes.
- Skipping working or changing notation part-way through a solution.
- Accepting an answer without checking its size, sign or units.
Exam Focus
Show the mathematical relationship you are using, keep notation consistent and give a clear final answer. Use a quick estimate, diagram or inverse operation to check that the result is reasonable.