Math lesson plan · 10th grade (Year 11 in England) · 60 minutes
Find angles with inverse trig
Trigonometry
CCSS HSG.SRT.C.8England: GCSE Higher Geometry
Objective and success criteria
Students will: Find angles with inverse trig.
- 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
Leads to: The sine rule (law of sines); Solve trigonometric equations; Find an angle with the sine rule
Materials: Scientific calculators, Protractors and rulers, Right-triangle diagrams, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 6 min
- Quick retrieval from earlier learning (Trigonometric ratios: SOH CAH TOA). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- A ramp rises at 23° over a horizontal distance of 7 m. How high does it rise? Give 1 decimal place. → 3Prompt: You know the adjacent side and want the opposite: use tan.
- A ramp rises at 51° over a horizontal distance of 9 m. How high does it rise? Give 1 decimal place. → 11.1Prompt: You know the adjacent side and want the opposite: use tan.
- A ramp rises at 49° over a horizontal distance of 4 m. How high does it rise? Give 1 decimal place. → 4.6Prompt: You know the adjacent side and want the opposite: use tan.
Hook · 6 min
- Show a ramp or a ladder against a wall and ask how steep it is.
- Share the objective: Find angles with inverse trig. Read the success criteria together.
I do: model it · 12 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: A right triangle has opposite side 7 cm and adjacent side 14 cm to angle θ. Find θ to 1 decimal place.
- Step 1: tan θ = 7/14
- Step 2: θ = tan⁻¹(7/14) ≈ 26.6°
- Answer: 26.6
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 12 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 right triangle has opposite side 13 cm and adjacent side 8 cm to angle θ. Find θ to 1 decimal place. → 58.4Prompt: Opposite and adjacent: use tan.
- In a right triangle the hypotenuse is 14 m and the side adjacent to angle θ is 3 m. Find θ to 1 decimal place. → 77.6Prompt: Adjacent and hypotenuse: use cos.
You do: independent practice · 17 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 · 7 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- In a right triangle the hypotenuse is 15 m and the side adjacent to angle θ is 4 m. Find θ to 1 decimal place. → 74.5Prompt: Adjacent and hypotenuse: use cos.
- A right triangle has opposite side 14 cm and adjacent side 15 cm to angle θ. Find θ to 1 decimal place. → 43Prompt: Opposite and adjacent: use tan.
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
- Move on to: The sine rule (law of sines); Solve trigonometric equations; Find an angle with the sine rule.
- 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-10.
Free lesson plan from eurekami.com/lesson-plan-builder