Year 10 - Maths
Checking and securing understanding of tangent ratio problems
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 the tangent ratio to find the missing side or angle in a right-angled triangle.
Key Notes
- The tangent ratio involves the opposite, adjacent and the angle
- If you know the length of the opposite and the size of the angle, you can use the tangent ratio
- If you know the length of the adjacent and the size of the angle, you can use the tangent ratio
- If you know the length of the opposite and adjacent, you can use the tangent ratio
Vocabulary To Learn
- Trigonometric functions: Trigonometric functions are commonly defined as ratios of two sides of a right-angled triangle containing the angle.
- Tangent function: The tangent of an angle (tan(θ°)) is the y-coordinate of point Q of the triangle which extends from the unit circle.
- Adjacent: The adjacent side of a right-angled triangle is the side which is next to both the right angle and the marked angle.
- Opposite: The opposite side of a right-angled triangle is the side which is opposite the marked angle.
Common Mistakes To Avoid
- Pupils may confuse the opposite and adjacent sides.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
The tangent ratio involves the opposite, adjacent and the angle. If you know the length of the opposite and the size of the angle, you can use the tangent ratio.
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 containing the 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 confuse the opposite and adjacent sides. Correction: The orientation of the right-angled triangle is not important. Identifying the known angle is what determines which is is the opposite and which is the adjacent.
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 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.