Trigonometry: SOH CAH TOA – Year 10 maths lesson

Lesson 9 of 37 in the Year 10 maths course

UK version. UK school years, UK spelling and pounds (£). · US Math Department

A complete 45-minute lesson for Year 10 (ages 14–15) 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 10 (ages 14–15)
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

45 minutes in 5 parts
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

All Year 10 maths lessons and tests · Maths Department

Curriculum

National Curriculum for England, Year 10: “apply Pythagoras’ Theorem and trigonometric ratios to find angles and lengths in right-angled triangles {and, where possible, general triangles} in 2 {and 3} dimensional figures”

National Curriculum for England, Year 10: “know the exact values of sin θ and cos θ for θ = 0°, 30°, 45°, 60° and 90°; know the exact value of tan θ for θ = 0°, 30°, 45°, 60°”

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Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.