Right triangle trigonometry – Grade 10 math lesson
Lesson 10 of 16 in the Grade 10 math course
US version. US grades, US spelling and dollars ($). · UK Maths Department
A complete 45-minute lesson for grade 10 (ages 15–16) that runs on this page – at school or at home. Every answer is graded right away, with a worked explanation.
- Time
- 45 minutes + 20 min homework
- Grade
- Grade 10 (ages 15–16)
- You need
- Paper, a pencil and this page
- Graded
- 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 graded straight away with a worked explanation, so you never have to grade 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
- Labeling 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
Learning goal: use sine, cosine and tangent to find sides and angles in right 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 | Graded by Classfern |
| Teaching input | 10 min | Not assessed, self-checked |
| Worked examples and guided practice | 9 min | Not assessed, graded by Classfern |
| Independent practice | 15 min | Graded by Classfern |
| Closure and exit ticket | 6 min | Graded by Classfern, self-checked |
Starter, "your turn", practice and exit ticket are graded 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 graded instantly.
More practice
More Grade 10 math lessons
- Factoring
- Quadratic equations
- Identities and proof
- Functions
- Graphing functions
- Exponential functions
- Circles: circumference and area
- Volume and surface area
- The Pythagorean theorem
- Transformations
- Similarity and congruence
- Properties of quadrilaterals
- Coordinate geometry
- Cross sections of 3-D figures
- Geometric constructions
Curriculum
Common Core State Standards HSG.SRT.C.8: “Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.*”
Common Core State Standards HSG.SRT.C.6: “Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.”
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.