---
type: "Chapter"
knowledge_type: "chapter"
entity_type: "chapter"
id: "69f869db293c3123114dafa6"
title: "Some Applications of Trigonometry"
board: "CBSE"
curriculum: "CBSE"
class: "Class 10"
subject: "Mathematics"
book: "Mathematics"
chapter: "Some Applications of Trigonometry"
chapter_slug: "some-applications-of-trigonometry"
canonical_url: "https://www.edzy.ai/cbse-class-10-mathematics-some-applications-of-trigonometry"
markdown_url: "https://www.edzy.ai/okf/chapter/cbse-class-10-mathematics-some-applications-of-trigonometry.md"
source_type: "examSubjectBookChapter"
source_id: "69f869db293c3123114dafa6"
source_pdf: "https://edzy-ai.s3.ap-south-1.amazonaws.com/edzy-express-ts/2f1b791e-5542-4bd3-8618-323a9e6a2070.pdf"
source: "Edzy"
version: 1
last_updated: "2026-06-20"
---

# Some Applications of Trigonometry
In this chapter, you will study how trigonometry is utilized to solve real-life problems involving heights and distances. By understanding concepts like the angle of elevation and angle of depression, you can determine unknown heights and distances based on given angles and measurements.

## Knowledge Snapshot
| Field | Details |
| :--- | :--- |
| Class | Class 10 |
| Subject | Mathematics |
| Book | Mathematics |
| Chapter | Some Applications of Trigonometry |
| Pages | 133-143 |

## Chapter Summary
### Short Summary
This chapter explores practical applications of trigonometry, especially in determining heights and distances through the concepts of angles of elevation and depression.

### Detailed Summary
The chapter begins with a discussion on how trigonometry is applied in real life, particularly in measuring heights and distances using the angle of elevation from an observer's eye level. The concept of the angle of depression is also introduced. Several problems are presented that illustrate how to calculate unknown heights and distances using trigonometric ratios and angles. Examples include determining the height of a tower, the positioning of ladders, and applications in real-world scenarios such as observing objects from different vantage points.

## Topic-Wise Explanation
### Heights and Distances
Heights and Distances involve calculating the height of an object or the distance to an object using trigonometric principles. Key measurements include the distance from the observer and the angle of elevation or depression.

### Angle of Elevation
The angle of elevation is the angle formed when an observer looks upwards at an object. It is crucial for calculating the height of tall structures based on the observer's distance.

### Angle of Depression
The angle of depression is formed when the observer looks down at an object. This angle helps in determining the height of the observer’s point of view above the object.

### Trigonometric Ratios Application
The application of trigonometric ratios, specifically sine, cosine, and tangent, is essential for solving problems related to heights and distances, allowing the calculation of unknown measures by using known angles and distances.

### Example Problems
The chapter includes multiple solved examples demonstrating practical applications, reinforcing concepts and techniques in trigonometry that students must understand.

### Height Calculation Techniques
Various techniques are used in calculating heights, including the use of trigonometric ratios to derive unknown lengths and heights from observed angles and distances.

## Core Ideas
| Idea | Explanation |
| :--- | :--- |
| Angle of Elevation | Used to find the height of objects above the observer's level. |
| Angle of Depression | Used to find the height of objects below the observer's level. |

## Key Concepts
| Concept | Meaning |
| :--- | :--- |
| Trigonometric Ratios | Ratios of the sides of a right triangle which include sine, cosine, and tangent. |

## Important Points for Revision
* The angle of elevation helps calculate the height of objects viewed above a horizontal line.
* The angle of depression helps calculate the height of objects viewed below a horizontal line.
* Trigonometric ratios are fundamental in determining unknown heights and distances.
* Both angles can be used in conjunction with known distances to derive heights.
* Example problems illustrate practical applications of trigonometry in real life.
* Understanding the observer's point and angle is crucial in determining correct measurements.

## Practice Questions
### Short Answer Questions
1. Define angle of elevation.
2. Define angle of depression.
3. Explain how to determine the height of a tower using an angle of elevation.
4. What trigonometric ratio is used to find the height when you know the angle of elevation?
5. How does the angle of depression help in determining distances?

### Long Answer Questions
1. Calculate the height of a 30 m tall building from an angle of elevation of 45° when observed 10 m away.
2. A man observes a tree at a distance of 25 m; the angle of elevation is 60°. Determine the height of the tree.
3. If the angle of depression from a point 10 m high to the ground is 30°, find the distance to the base of the object viewed.

## Related Concepts
* Trigonometric Ratios
* Right Triangle Properties

## Source Attribution
| Field | Value |
| :--- | :--- |
| Source | Edzy |
| Reference Type | examSubjectBookChapter |
| Reference ID | 69f869db293c3123114dafa6 |
| Canonical URL | https://www.edzy.ai/cbse-class-10-mathematics-some-applications-of-trigonometry |
| Markdown URL | https://www.edzy.ai/okf/chapter/cbse-class-10-mathematics-some-applications-of-trigonometry.md |