Year 10 - Maths
Applying Pythagoras' theorem in 3D
Right-angled trigonometry
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Study Guides
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 apply knowledge of Pythagoras' theorem to 3D problems.
Key Notes
- For packing efficiency, it can be useful to know the length of the longest diagonal
- This would be from a bottom corner of a rectangular box, to the opposite top corner
- You can construct a right-angled triangle to calculate this
- You will need to know the length of the diagonal of the base of the box
- There is a formula you can deduce to calculate the longest diagonal
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.
- Cross-section: A cross-section is a 2D face made from cutting straight through any plane of a 3D object.
Common Mistakes To Avoid
- Pythagoras' theorem cannot be applied to 3D shapes.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
For packing efficiency, it can be useful to know the length of the longest diagonal. This would be from a bottom corner of a rectangular box, to the opposite top corner.
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: Pythagoras' theorem cannot be applied to 3D shapes. Correction: Pupils may benefit from imaging the cuboid is 'sliced' through and a triangle drawn on the now visible face.
More Lessons In This Unit
- Advanced problem solving with right-angled trigonometry 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
- Using Pythagoras' theorem to justify a right-angled triangle Study Guide
Browse all guides in the Year 10 Maths guide library.