Year 10 - Maths
Checking and securing understanding of sine ratio problems
Right-angled trigonometry
Study Hub
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 use the sine ratio to find the missing side or angle in a right-angled triangle.
Key Notes
- The sine ratio involves the hypotenuse, opposite and the angle
- If you know the length of the hypotenuse and the size of the angle, you can use the sine ratio
- If you know the length of the opposite and the size of the angle, you can use the sine ratio
- If you know the length of the hypotenuse and opposite, you can use the sine ratio
Vocabulary To Learn
- Hypotenuse: The hypotenuse is the side of a right-angled triangle which is opposite the right angle.
- Opposite: The opposite side of a right-angled triangle is the side which is opposite the marked angle.
- 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.
Common Mistakes To Avoid
- Incorrectly rearranging the sine formula.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
The sine ratio involves the hypotenuse, opposite and the angle. If you know the length of the hypotenuse and the size of the angle, you can use the sine ratio.
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 the sine formula. Correction: A ratio table can be helpful to see the relationship between the sides and therefore how to rearrange.
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 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.