Math lesson plan · 10th grade (Year 11 in England) · 45 minutes
Find a side when it is on the bottom of the trig ratio
Trigonometry
CCSS HSG.SRT.C.8England: GCSE Higher Geometry
Objective and success criteria
Students will: Find a side when it is on the bottom of the trig ratio.
- 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 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). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- A ramp rises at 29° over a horizontal distance of 16 m. How high does it rise? Give 1 decimal place. → 8.9Prompt: You know the adjacent side and want the opposite: use tan.
- A ramp rises at 69° over a horizontal distance of 10 m. How high does it rise? Give 1 decimal place. → 26.1Prompt: You know the adjacent side and want the opposite: use tan.
- A ramp rises at 41° over a horizontal distance of 17 m. How high does it rise? Give 1 decimal place. → 14.8Prompt: You know the adjacent side and want the opposite: use tan.
Hook · 5 min
- Show a ramp or a ladder against a wall and ask how steep it is.
- Share the objective: Find a side when it is on the bottom of the trig ratio. 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: In a right triangle, the side adjacent to a 52° angle is 19 cm. Find the hypotenuse to 1 decimal place.
- Step 1: H = 19 ÷ cos 52°
- Step 2: ≈ 30.9 cm
- Answer: 30.9
- 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.
- In a right triangle, the side adjacent to a 54° angle is 25 cm. Find the hypotenuse to 1 decimal place. → 42.5Prompt: cos = A/H: the unknown H is on the bottom.
- Kai flies a drone 12 m above the ground. From where Kai stands, the angle of elevation to the drone is 54°. How far horizontally is the drone from Kai? Give 1 decimal place. → 8.7Prompt: The height is opposite the angle; the horizontal distance is adjacent.
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.
- Nia flies a drone 10 m above the ground. From where Nia stands, the angle of elevation to the drone is 60°. How far horizontally is the drone from Nia? Give 1 decimal place. → 5.8Prompt: The height is opposite the angle; the horizontal distance is adjacent.
- In a right triangle, the side opposite a 41° angle is 17 cm. Find the hypotenuse to 1 decimal place. → 25.9Prompt: sin = O/H: the unknown H is on the bottom.
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-10.
Free lesson plan from eurekami.com/lesson-plan-builder