Year 10 - Maths
Using Pythagoras' theorem to justify a right-angled triangle
Right-angled 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 are introduced to a variety of situations where trigonometric ratios are required, such as 3-D problems and problems of elevation or depression.
Lesson Summary
You will learn to use Pythagoras' theorem to justify whether a triangle is right-angled.
Key Notes
- For a triangle to be right-angled, Pythagoras' theorem must hold
- By substituting in the three lengths, you can show whether the theorem holds
- If the numbers produce a true statement, the triangle is right-angled
- If they do not produce a true statement, the triangle is not right-angled
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
- Incorrectly rearranging Pythagoras' theorem.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
For a triangle to be right-angled, Pythagoras' theorem must hold. By substituting in the three lengths, you can show whether the theorem holds.
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: Incorrectly rearranging Pythagoras' theorem. Correction: It can be helpful to scaffold the steps for any pupils who are struggling with rearranging.
More Lessons In This Unit
- Advanced problem solving with right-angled trigonometry Study Guide
- Applying Pythagoras' theorem in 3D Study Guide
- Applying trigonometric ratios in 3D Study Guide
- Applying trigonometric ratios in context Study Guide
- Calculate trigonometric ratios for 0°, 45° and 90° Study Guide
- Calculate trigonometric ratios for 30° and 60° Study Guide
- Calculating the length of a line segment Study Guide
- Checking and further securing understanding of Pythagoras' theorem Study Guide
- Checking and securing understanding of cosine problems Study Guide
- Checking and securing understanding of sine ratio problems Study Guide
- Checking and securing understanding of tangent ratio problems Study Guide
- Checking and securing understanding of the unit circle Study Guide
- Problem solving with right-angled trigonometry Study Guide
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