Year 10 - Maths
Problem solving with right-angled trigonometry
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 your knowledge of right-angled trigonometry to solve problems.
Key Notes
- Sometimes an answer may be best left in an exact form
- When dealing with right-angled trigonometry, it is important to look at the information you have and can deduce
- Consider whether Pythagoras' theorem or trigonometric ratios are more efficient to use
Vocabulary To Learn
- Trigonometric functions: Trigonometric functions are commonly defined as ratios of two sides of a right-angled triangle for a given angle.
- Sine function: The sine of an angle (sin(θ°)) is the y-coordinate of point P on the triangle formed inside the unit circle.
- Cosine function: The cosine of an angle (cos(θ°)) is the x-coordinate of point P on the triangle formed inside the unit circle.
- Tangent function: The tangent of an angle (tan(θ°)) is the y-coordinate of point Q on the triangle which extends from the unit circle.
Common Mistakes To Avoid
- Pupils may not be confident in knowing whether to apply Pythagoras' theorem or a trigonometric ratio.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Sometimes an answer may be best left in an exact form. When dealing with right-angled trigonometry, it is important to look at the information you have and can deduce.
2. Use this key word in a maths sentence and explain it clearly. 'Trigonometric functions'
Trigonometric functions are commonly defined as ratios of two sides of a right-angled triangle for a given 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 not be confident in knowing whether to apply Pythagoras' theorem or a trigonometric ratio. Correction: Encourage pupils to label the diagram with all the information they have and then consider what they can deduce.
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
- Using Pythagoras' theorem to justify a right-angled triangle Study Guide
Browse all guides in the Year 10 Maths guide library.