Math lesson plan · 10th grade (Year 11 in England) · 30 minutes
Find exact side lengths using 30°, 45° and 60°
Trigonometry
CCSS HSG.SRT.C.6CCSS HSG.SRT.C.8England: GCSE Higher Geometry
Objective and success criteria
Students will: Find exact side lengths using 30°, 45° and 60°.
- 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: Exact trig values (0°, 30°, 45°, 60°, 90°)
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 · 4 min
- Quick retrieval from earlier learning (Exact trig values (0°, 30°, 45°, 60°, 90°)). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- What is the exact value of cos 45°? (√3/2 / √3/3 / √2/2 / 1) → √2/2Prompt: Use the 30-60-90 triangle (sides 1, √3, 2) or the 45-45-90 triangle (sides 1, 1, √2).
- What is the exact value of tan 30°? (1/2 / √3/3 / 1 / √3/2) → √3/3Prompt: Use the 30-60-90 triangle (sides 1, √3, 2) or the 45-45-90 triangle (sides 1, 1, √2).
- What is the exact value of sin 0°? (√2/2 / 0 / √3 / 1) → 0Prompt: Use the 30-60-90 triangle (sides 1, √3, 2) or the 45-45-90 triangle (sides 1, 1, √2).
Hook · 3 min
- Show a ramp or a ladder against a wall and ask how steep it is.
- Share the objective: Find exact side lengths using 30°, 45° and 60°. Read the success criteria together.
I do: model it · 7 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: A right triangle has two equal sides of 9 cm and a 45° angle. Find the hypotenuse. Give an exact answer.
- Step 1: 9 ÷ (√2/2) = 9√2
- Step 2: 9√2 cm
- Answer: 9√2
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 6 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 two equal sides of 8 cm and a 45° angle. Find the hypotenuse. Give an exact answer. → 8√2Prompt: Use the exact value cos 45° = √2/2.
- An equilateral triangle has sides of 6 cm. Find its exact height. → 3√3Prompt: The height splits it into two 30°-60°-90° triangles.
You do: independent practice · 7 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 6 questions are on the student sheet below, with answers in the key.
Exit ticket · 3 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- An equilateral triangle has sides of 2 cm. Find its exact height. → √3Prompt: The height splits it into two 30°-60°-90° triangles.
- A right triangle has two equal sides of 7 cm and a 45° angle. Find the hypotenuse. Give an exact answer. → 7√2Prompt: Use the exact value cos 45° = √2/2.
Watch out for
- Mixing up opposite and adjacent sides.
- Calculator in radians instead of degrees.
Support and stretch
Support
- Review first: Exact trig values (0°, 30°, 45°, 60°, 90°).
- 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