Year 10 - Maths
Checking and further securing understanding of Pythagoras' theorem
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 calculate the length of a 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
- The difference between the squares of the longest and known shorter sides is the square of the remaining side
- A calculator can perform these calculations efficiently
- Rounding gives a less accurate answer so there might be times you wish to leave your answer with an operator
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
- Misidentifying the hypotenuse.
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: Misidentifying the hypotenuse. Correction: The hypotenuse is the longest side of a right-angled triangle. It is always opposite the right-angle.
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 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
- Using Pythagoras' theorem to justify a right-angled triangle Study Guide
Browse all guides in the Year 10 Maths guide library.