Math lesson plan · 11th grade (Year 12 in England) · 45 minutes
Solve bearings problems with trigonometry
Trigonometry
CCSS HSG.SRT.C.8England: GCSE Higher Geometry
Objective and success criteria
Students will: Solve bearings problems with trigonometry.
- I can answer questions on today's skill on my own, without help.
- I can explain each step and say why it works.
- I can check my answer and spot a mistake.
Before and after
Needs first: Trigonometric ratios: SOH CAH TOA; Find a side with the cosine rule
Leads to: the next skill in this area.
Materials: Scientific calculators, Protractors and rulers, Right-triangle diagrams, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 5 min
- Quick retrieval from earlier learning (Trigonometric ratios: SOH CAH TOA; Find a side with the cosine rule). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- In triangle ABC, b = 11 cm, c = 9 cm and A = 54°. Find a to 1 decimal place. → 9.3Prompt: a² = b² + c² − 2bc cos A.
- In triangle ABC, b = 17 cm, c = 20 cm and A = 79°. Find a to 1 decimal place. → 23.6Prompt: a² = b² + c² − 2bc cos A.
- In triangle ABC, b = 7 cm, c = 17 cm and A = 29°. Find a to 1 decimal place. → 11.4Prompt: a² = b² + c² − 2bc cos A.
Hook · 5 min
- Show a ramp or a ladder against a wall and ask how steep it is.
- Share the objective: Solve bearings problems with trigonometry. Read the success criteria together.
I do: model it · 10 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: A boat sails 45 km on a bearing of 043°. How far east of its start is it? Give 1 decimal place.
- Step 1: 45 × sin 43° ≈ 30.7 km
- Answer: 30.7
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 10 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- A boat sails 33 km on a bearing of 056°. How far east of its start is it? Give 1 decimal place. → 27.4Prompt: Bearings are measured clockwise from north.
- The bearing of B from A is 026°. What is the bearing of A from B? → 206Prompt: The return direction is exactly opposite.
You do: independent practice · 10 min
- Students work on the student sheet. Circulate and check the first two answers of every student early.
- Students who finish: write a question of their own for a partner, with the answer.
The 8 questions are on the student sheet below, with answers in the key.
Exit ticket · 5 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Two drones leave a base. One flies 27 km on a bearing of 064°, the other 10 km on a bearing of 150°. How far apart are they? Give 1 decimal place. → 28.1Prompt: The angle between their paths is the difference of the bearings.
- A boat sails 24 km on a bearing of 057°. How far east of its start is it? Give 1 decimal place. → 20.1Prompt: Bearings are measured clockwise from north.
Watch out for
- Mixing up opposite and adjacent sides.
- Calculator in radians instead of degrees.
Support and stretch
Support
- Review first: Trigonometric ratios: SOH CAH TOA.
- Use concrete materials: scientific calculators.
- Give the first step of each question, or a partly worked example to finish.
- Pair with a confident partner for the guided practice.
Stretch
- Explain a common mistake in writing and how to fix it.
- Write a word problem that uses today's skill, then solve a partner's.
Homework and more practice
Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-11.
Free lesson plan from eurekami.com/lesson-plan-builder