NCERT Class 10 Mathematics Mathematics: Chapter 8 — 1 Introduction
This chapter introduces the fundamental concepts of trigonometry, a branch of mathematics dealing with the relationships between the sides and angles of triangles. It begins by presenting real-world scenarios where right triangles can be visualized, such as measuring the height of Qutub Minar or the width of a river. The text explains that trigonometry, derived from Greek words meaning 'three-sided measure', was historically used by astronomers and is now crucial in engineering and physical sciences. The chapter focuses on defining trigonometric ratios with respect to acute angles in a right triangle, introducing terms like 'opposite side' and 'adjacent side'. It also mentions the extension of these ratios to angles of 0° and 90°, and the establishment of trigonometric identities. This foundational knowledge is essential for further study in mathematics and its applications.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 10 |
| Subject | Mathematics |
| Book | Mathematics |
| Chapter | Chapter 8 — 1 Introduction |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 3 minutes |
| Word count | 571 |
Learning outcomes
- Understand the definition and origin of trigonometry.
- Identify right triangles in real-world contexts.
- Define and understand the terms 'opposite side' and 'adjacent side' with respect to acute angles in a right triangle.
- Recognize the importance of trigonometry in various fields like engineering and physical sciences.
- Prepare for understanding trigonometric ratios for specific angles and identities.
Vocabulary
| Word | Meaning |
|---|---|
| Trigonometry | The study of relationships between the sides and angles of a triangle. |
| Right triangle | A triangle with one angle measuring 90 degrees. |
| Acute angle | An angle less than 90 degrees. |
| Hypotenuse | The side opposite the right angle in a right triangle. |
| Opposite side | The side facing a particular angle in a right triangle. |
| Adjacent side | The side next to a particular angle in a right triangle, which is not the hypotenuse. |
The complete chapter text is read in the official NCERT PDF viewer below (streamed from ncert.nic.in). This page provides NCERT Help study material — summary, vocabulary, practice questions, and FAQs — not a full reproduction of the textbook.
Read chapter online
This PDF is loaded from the official NCERT website (ncert.nic.in). Use the page buttons below to read — download is disabled on NCERT Help.
Read page by page below. PDF is streamed from the official NCERT website — no download button on this page.
Practice questions
- What is the meaning of the word 'trigonometry'? Answer: Trigonometry is derived from Greek words meaning 'three', 'sides', and 'measure', hence it is the study of relationships between the sides and angles of a triangle.
- Give an example of a situation where a right triangle can be imagined. Answer: A student looking at the top of Qutub Minar forms a right triangle.
- In a right triangle ABC, with angle A being acute, what is the side opposite to angle A? Answer: The side BC is opposite to angle A.
- What is the hypotenuse in a right triangle ABC? Answer: The side AC is the hypotenuse.
Frequently asked questions
What is trigonometry?
Trigonometry is a branch of mathematics that studies the relationships between the sides and angles of triangles.
Where is trigonometry used?
Trigonometry is used in engineering, physical sciences, astronomy, and many other technologically advanced fields.
What are the basic components of a right triangle in trigonometry?
The basic components are the hypotenuse, the side opposite to an angle, and the side adjacent to an angle.
What does the word 'trigonometry' mean?
It comes from Greek words: 'tri' (three), 'gon' (sides), and 'metron' (measure).
What type of angles are primarily discussed in this chapter's introduction to trigonometric ratios?
The chapter focuses on acute angles (angles less than 90 degrees).
What is the hypotenuse in a right triangle?
The hypotenuse is the longest side of a right triangle, opposite the right angle.
Related resources
Important topics
Topics covered
NCERT Class 10 Mathematics — Mathematics — Chapter 8 — 1 Introduction. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.