Year 10 - Maths
Calculating the length of a line segment
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 calculate the length of a line segment on a coordinate grid in all four quadrants or using the coordinate pairs.
Key Notes
- Any line segment can be turned into a right-angled triangle by adding two lines which meet at 90°
- Calculating the horizontal distance gives the length of one side
- Calculating the vertical distance gives the length of the other side
- These two shorter sides lengths can be used to calculate the length of the line segment
- This can be done using Pythagoras' theorem
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 think that direction matters when determining the distance between two points.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Any line segment can be turned into a right-angled triangle by adding two lines which meet at 90°. Calculating the horizontal distance gives the length of one side.
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 think that direction matters when determining the distance between two points. Correction: Direction matters when dealing with displacement, not distance.
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
- 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
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