NCERT Class 10 Mathematics Mathematics: Chapter 9 — 1 Heights and Distances
This chapter, 'Some Applications of Trigonometry', builds upon the trigonometric ratios studied previously. It introduces practical applications of trigonometry in real-life scenarios. Key concepts include the 'line of sight', which is the line from an observer's eye to the object being viewed. The 'angle of elevation' is defined as the angle formed by the line of sight with the horizontal when the object is above the horizontal level, requiring the observer to look upwards. Conversely, the 'angle of depression' is formed when the object is below the horizontal level, requiring the observer to look downwards. The chapter emphasizes that to calculate heights or distances without direct measurement, specific information like the distance from the object and angles is necessary. This chapter helps students apply trigonometric principles to solve real-world problems, enhancing their understanding of mathematics in practical contexts.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 10 |
| Subject | Mathematics |
| Book | Mathematics |
| Chapter | Chapter 9 — 1 Heights and Distances |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 2 minutes |
| Word count | 395 |
Learning outcomes
- Understand the concepts of line of sight, angle of elevation, and angle of depression.
- Apply trigonometric ratios to solve problems involving heights and distances.
- Relate trigonometry to real-world situations.
- Calculate unknown heights and distances using given angles and distances.
Vocabulary
| Word | Meaning |
|---|---|
| Trigonometric ratios | Ratios of sides of a right-angled triangle (sine, cosine, tangent, etc.). |
| Line of sight | The line drawn from the eye of an observer to the point of an object being viewed. |
| Angle of elevation | The angle formed by the line of sight with the horizontal when the object is above the horizontal level. |
| Angle of depression | The angle formed by the line of sight with the horizontal when the object is below the horizontal level. |
| Horizontal level | A line parallel to the ground or the observer's eye level. |
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Practice questions
- What is the line of sight? Answer: The line drawn from the eye of an observer to the point in the object viewed by the observer.
- When is the angle of elevation formed? Answer: The angle of elevation is formed when the point being viewed is above the horizontal level, and the observer raises their head.
- Define the angle of depression. Answer: The angle of depression is the angle formed by the line of sight with the horizontal when the point being viewed is below the horizontal level, and the observer lowers their head.
- What information is needed to find the height of a minar without measuring it directly? Answer: The distance from the observer to the foot of the minar and the angle of elevation are needed.
Frequently asked questions
What is the main topic of Chapter 9 in NCERT Class 10 Mathematics?
Chapter 9 of NCERT Class 10 Mathematics is about 'Some Applications of Trigonometry', focusing on heights and distances.
What is the difference between angle of elevation and angle of depression?
The angle of elevation is when you look up at an object above your horizontal level, while the angle of depression is when you look down at an object below your horizontal level.
What is a 'line of sight' in trigonometry?
The line of sight is the imaginary line connecting the observer's eye to the point they are looking at on an object.
Can trigonometry be used to measure heights of tall structures?
Yes, trigonometry is very useful for calculating heights of tall structures like buildings or mountains without direct measurement, using angles and distances.
What kind of information is needed to solve problems in this chapter?
Typically, you need to know at least one distance and one angle, or two distances, to solve problems involving heights and distances using trigonometry.
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NCERT Class 10 Mathematics — Mathematics — Chapter 9 — 1 Heights and Distances. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.