Trigonometry: SOH CAH TOA – Year 9 maths lesson
Lesson 14 of 38 in the Year 9 maths course
UK version. UK school years, UK spelling and pounds (£). · US Math Department
A complete 45-minute lesson for Year 9 (ages 13–14) that runs on this page – at school or at home. Every answer is marked straight away, with a worked explanation.
- Time
- 45 minutes + 20 min homework
- Year
- Year 9 (ages 13–14)
- You need
- Paper, a pencil and this page
- Marked
- Instantly, with explanations
For parents: how to use this lesson
You don't need to know this topic yourself. The lesson explains each step on screen, one tidy step at a time. Every answer is marked straight away with a worked explanation, so you never have to mark anything.
- Read what your child will learn and the big ideas together.
- Press Start the lesson below and sit with your child for the teaching and the worked examples (about 19 minutes).
- Let them do the practice on their own. They choose Getting started, On track or Challenge – start on On track and move up after a few right in a row.
- Finish with the exit ticket and the talk question: “How could you find the height of a building without climbing it?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Labelling sides from the wrong angle. Mark the angle first, then label opposite and adjacent.
- Calculator in radians. Check it shows D (degrees).
Tip for home: Estimate heights of trees or lamp posts using an angle and a distance.
What your child will learn
We are learning to use sine, cosine and tangent to find sides and angles in right-angled triangles.
Success looks like
- I can label the sides.
- I can find a missing side.
- I can find a missing angle.
Key words
- opposite
- the side across from the angle
- adjacent
- the side next to the angle (not the hypotenuse)
- hypotenuse
- the longest side
- inverse
- sin⁻¹, cos⁻¹, tan⁻¹ find the angle
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Use a protractor and a tape measure to estimate the height of a tree or building with tan.
The big ideas (for the adult)
Label the sides from the angle you are using: opposite, adjacent and hypotenuse.
SOH CAH TOA: sin = opposite ÷ hypotenuse, cos = adjacent ÷ hypotenuse, tan = opposite ÷ adjacent.
To find an angle, use the inverse: θ = sin⁻¹(opposite ÷ hypotenuse). Learn the exact values for 30°, 45° and 60°.
The lesson, step by step
| Part | Time | How it is checked |
|---|---|---|
| Starter: quick recall | 5 min | Marked by Classfern |
| Teaching input | 10 min | Not assessed, self-checked |
| Worked examples and guided practice | 9 min | Not assessed, marked by Classfern |
| Independent practice | 15 min | Marked by Classfern |
| Plenary and exit ticket | 6 min | Marked by Classfern, self-checked |
Starter, "your turn", practice and exit ticket are marked by Classfern. Worked examples and teaching are not assessed. The hands-on task and the reflection are self-assessed. Explanations in talk are judged by the parent and not recorded.
The lesson
It runs here on the page. No sign-up and no names – progress is kept only in this browser.
Homework and practice at home
20 minutes: 10 practice questions, 3 multiple-choice questions and 2 to remember from earlier work, then a short reflection. New questions every time, all marked instantly.
More practice
More Year 9 maths lessons
- Prime factors, HCF and LCM
- Rounding and estimation
- Bounds and error intervals
- Standard form
- Laws of indices
- Powers and roots
- Units and measures
- Area of triangles, parallelograms and trapeziums
- Circles: circumference, area, arcs and sectors
- Volume and surface area
- Angle facts and parallel lines
- Angles in polygons
- Pythagoras' theorem
- Transformations
- Similarity and congruence
- Quadrilaterals and symmetry
- Coordinate geometry
- 3-D shapes, plans and elevations
- Quartiles, box plots and spread
- Pie charts and time series graphs
- Sampling
- Relative frequency and expected outcomes
- Venn diagrams and conditional probability
- Algebraic notation
- Substitution
- Simplifying expressions
- Expanding brackets
- Solving linear equations
- Inequalities
- Rearranging formulae
- Sequences and the nth term
- Straight-line graphs
- Graphs of functions
- Ratio
- Percentages
- Speed, density and pressure
- Scale drawings and maps
Curriculum
National Curriculum for England, Year 9: “use Pythagoras’ Theorem and trigonometric ratios in similar triangles to solve problems involving right-angled triangles”
GCSE subject content G20: “know the formulae for: Pythagoras’ theorem, a² + b² = c², and the trigonometric ratios, sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse and tan θ = opposite/adjacent; apply them to find angles and lengths in right-angled triangles and, where possible, general triangles in two and three dimensional figures”
Contains public sector information licensed under the Open Government Licence v3.0.
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.