Year 9 - Maths
Checking and securing understanding of Pythagoras' theorem
Trigonometry
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit pupils learn how to recognise the relationship between the unit circle and the trigonometric ratios of sine, cosine and tangent. Pupils then apply this knowledge to solve trigonometric problems.
Lesson Summary
You will learn to use Pythagoras' theorem to find the length of any side of a right-angled triangle.
Key Notes
- The sum of the squares of the two shorter sides equals the square of the longest side.
- The longest side is always opposite the right angle.
- a^2+b^2=c^2 can be rearranged to find one of the shorter side lengths.
- If the right-angled triangle is not immediately available, see if you can construct one.
Vocabulary To Learn
- Hypotenuse: The hypotenuse is the side of a right-angled triangle which is opposite the right angle.
- Pythagoras' theorem: Pythagoras' theorem states that the sum of the squares of the two shorter sides of a right-angled triangle is equal to the square of the hypotenuse.
Common Mistakes To Avoid
- Pupils may find it initially difficult to see how Pythagoras' theorem can be used when a right-angled triangle is not immediately available.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
The sum of the squares of the two shorter sides equals the square of the longest side. The longest side is always opposite the right angle.
2. Use this key word in a maths sentence and explain it clearly. 'Hypotenuse'
The hypotenuse is the side of a right-angled triangle which is opposite the right angle. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Pupils may find it initially difficult to see how Pythagoras' theorem can be used when a right-angled triangle is not immediately available. Correction: Encourage pupils to draw their own diagram in cases where there is not one provided. In cases where pairs of coordinates are being used, encourage pupils to draw on horizontal and vertical line segments.
More Lessons In This Unit
- Checking and securing understanding of similar triangles Study Guide
- Choosing an appropriate method for finding lengths of a triangle Study Guide
- Choosing the right trigonometric ratio Study Guide
- Problem solving with trigonometry Study Guide
- Scaling the right-angled triangle from the unit circle Study Guide
- Sine and cosine ratios Study Guide
- Tangent ratio Study Guide
- The unit circle Study Guide
- Using the cosine ratio Study Guide
- Using the sine ratio Study Guide
- Using the tangent ratio Study Guide
Browse all guides in the Year 9 Maths guide library.