NCERT Exemplar for Class 10 Maths Chapter 9- Some Applications of Trigonometry for 2024-25 Board Exams:
Students may download NCERT Exemplar Class 10 Maths Chapter 9 Some Applications of Trigonometry in pdf format and use it to prepare for CBSE examinations. Maths professionals have created these sample problems and solutions following the most recent syllabus of CBSE (2024-2025).
Students may acquire a free PDF of these answered problems and use it to understand better the essential formulae and practice questions of Trigonometry to improve their Maths abilities.
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All of the problems in the NCERT Textbook's Chapter 9: Some Applications of Trigonometry are fully addressed in the NCERT Solutions for Class 10 Maths. Due to the concepts' clarity and organization, NCERT Solutions will boost students' confidence and help them do well in the CBSE 2025 exams. Our subject matter expert draught and review the solutions, which are then updated in accordance with the most recent CBSE Syllabus for 2024–2025 and the CBSE board's regulations.
It covers every chapter and offers chapter-by-chapter answers. These NCERT Solutions for Class 10 Maths assist students by addressing their questions and giving each idea a solid basis.
Out of the total 80 points for the Class 10 CBSE Maths exam, 12 are for the chapter on trigonometry. There will be 1 question in this chapter. The paper is divided into 4 sections, each with a unique mark. The questions were given one mark, two marks, three marks, and four marks.
NCERT Exemplar for Class 10 Maths Chapter 9- Some Applications of Trigonometry | Free PDF Download
NCERT Exemplar Solutions Class 10 of All Chapters:
NCERT EXEMPLAR SOLUTIONS CLASS 10 CHAPTER 1 REAL NUMBERS
NCERT EXEMPLAR SOLUTIONS CLASS 10 CHAPTER 2 POLYNOMIALS
NCERT EXEMPLAR SOLUTIONS CLASS 10 CHAPTER 3 PAIR OF LINEAR EQUATIONS IN 2 VARIABLES
NCERT EXEMPLAR SOLUTIONS CLASS 10 CHAPTER 4 QUADRATIC EQUATIONS
NCERT EXEMPLAR SOLUTIONS CLASS 10 CHAPTER 5 ARITHMETIC PROGRESSIONS
NCERT EXEMPLAR SOLUTIONS CLASS 10 CHAPTER 6 TRIANGLES
NCERT EXEMPLAR SOLUTIONS CLASS 10 CHAPTER 7 COORDINATE GEOMETRY
NCERT EXEMPLAR SOLUTIONS CLASS 10 CHAPTER 8 INTRODUCTION TO TRIGONOMETRY & ITS EQUATION
NCERT EXEMPLAR SOLUTIONS CLASS 10 CHPATER 9 SOME APPLICATIONS OF TRIGONOMETRY
NCERT EXEMPLAR SOLUTIONS CLASS 10 CHAPTER 10 CIRCLES
NCERT EXEMPLAR SOLUTIONS CLASS 10 CHAPTER 11 CONSTRUCTIONS
NCERT EXEMPLAR SOLUTIONS CLASS 10 CHAPTER 12 AREAS RELATED TO CIRCLES
NCERT EXEMPLAR SOLUTIONS CLASS 10 CHAPTER 13 SURFACE AREAS AND VOLUMES
NCERT EXEMPLAR SOLUTIONS CLASS 10 CHAPTER 14 STATISTICS AND PROBABILITY
NCERT EXEMPLAR SOLUTIONS CLASS 10 CHAPTER 15 PROBABILITY
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The NCERT Exemplar Solutions for Chapter 9 Some Applications of Trigonometry for Class 10 students includes four exercises.
9.1 Introduction
You learned about trigonometric ratios in the previous chapter. You'll learn about various applications of trigonometry in this chapter that affect your daily life. One of the oldest disciplines still being studied by academics today is trigonometry. Trigonometry was created because astronomy had a need for it, as we have learned in Chapter 8 of this book. This chapter will demonstrate how trigonometry may be used to determine various objects' heights and distances without actually measuring them.
9.2 Elevations and Radius
Line of sight, angle of deviation, angle of elevation, and angle of depression are all covered in this topic. Solving a few issues explains all the procedures. Trigonometric ratios are used to address the numerical issues.
9.3 Synopsis or summary
All of the topics covered in the chapter are included in the summary. You will be better able to comprehend the key ideas that the remainder of the chapter needs to concentrate on. In order to fully understand the important ideas in Class 10 Maths Chapter 9, students can make use of the NCERT Solutions for Class 10. These solutions have been created by knowledgeable instructors to provide clarity on important ideas and problem-solving abilities.
CBSE SAMPLE PAPER CLASS 10 FOR UPCOMING BOARD EXAMS | FREE PDF DOWNLOAD
Students may also utilize this NCERT Exemplar to complete even the most challenging problems and prepare for examinations. However, sample papers and previous year's question papers are quite helpful in understanding the sorts of questions a paper setter asked in the examination from this chapter 12 and the marking system.
Students in class 10 will learn how trigonometry may be used to determine the height and distance of various objects without measuring them in this chapter, "Some applications of trigonometry." Trigonometry has historically been used by astronomers to determine how far away the planets and stars are from Earth. To determine a point in reference to latitude and longitude, trigonometry is mostly employed in navigation and geography.
Trigonometry applications will be taught to students in a more effective way by using examples from everyday life. The key concepts and issues are clarified using geometrical illustrations, and a summary is provided at the chapter's conclusion. You are given step-by-step method answers to all of the problems in the NCERT Solutions for Class 10 Maths.
Key Elements of NCERT Solutions for Class 10 Maths Chapter 9: Some Trigonometry Applications
- Specialists in the relevant fields created the solutions.
- Access to questions and answers is broken down in each chapter.
- Good advice for pupils getting ready for the CBSE 2024-25
- The thorough method includes explanations of the solutions.
- All the workout solutions are readily available.
To help students become more adept at handling problems, the knowledgeable faculty staff has created clear NCERT Solutions. Students can use the study resources offered by our website to have a clearer understanding of certain applications of trigonometry.
Students in the tenth grade are also given online study tools, including notes, example books, NCERT answers, and question papers, to help them prepare for the board examinations.
This chapter may take some time to complete, and students must pay close attention. The NCERT Exemplar for Class 10 Maths is provided by our website to assist students in solving chapter concerns and obtaining proper answers to complex questions.
Students in class 10 will learn how to use trigonometry to estimate the height and distance of various objects without having to measure them in chapter 9, "Some Applications of Trigonometry." Astronomers once utilised trigonometry to calculate the separation between the planets, the earth, and other stars. Trigonometry is most typically used in geography and navigation to determine the latitude and longitude of a given point.
In this chapter, students will be able to study about heights and distances, the line of sight, the angle of elevation, the horizontal line, and the angle of depression. By solving the problems, students may gain a thorough understanding of the subjects. In this chapter, all of the numerical issues are resolved using trigonometric ratios.
Horizontal Altitude or Level and Line of Sight
The line traced from an observer's eye to the spot on the thing they are viewing is known as their line of sight. The horizontal level is the line that runs through the observer's sight.
The depression's angle
When considering things below the horizontal level, the angle of depression is important. The line of sight's angle with the horizontal level is what we are talking about.
Height and Distance Calculations
Trigonometric ratios can be used to compute heights and distances.
Consult the trigonometric ratio table below for further information.
|
TRIGONOMETRIC RATIOS TABLE |
|
|
|
|
|
|
|
|
|
Angles (In Degrees) |
0° |
30° |
45° |
60° |
90° |
180° |
270° |
360° |
|
Angles (In Radians) |
0° |
π/6 |
π/4 |
π/3 |
π/2 |
π |
3π/2 |
2π |
|
Sin |
0 |
1/2 |
1/√2 |
√3/2 |
1 |
0 |
-1 |
0 |
|
Cos |
1 |
√3/2 |
1/√2 |
1/2 |
0 |
-1 |
0 |
1 |
|
Tan |
0 |
1/√3 |
1 |
√3 |
∞ |
0 |
∞ |
0 |
|
Cot |
∞ |
√3 |
1 |
1/√3 |
0 |
∞ |
0 |
∞ |
|
Cosec |
∞ |
2 |
√2 |
2/√3 |
1 |
∞ |
-1 |
∞ |
|
sec |
1 |
2/√3 |
√2 |
2 |
∞ |
-1 |
∞ |
1 |
Step 1: First, create a line diagram that corresponds to the issue.
Step 2: Mark all known angles, heights, and distances, and use variables to indicate any lengths that are unknown.
Step 3: Subtract the known lengths from the unknown lengths using the values of various trigonometric ratios of the angles.
Trigonometric distance calculations for determining the distances between celestial bodies
The parallax technique may be used to measure vast distances. When an item is seen from two separate places, the parallax angle, which is half the angle between the two lines of sights, is present. Large distances may be estimated by knowing the parallax angle and the separation between the two sites.
The chapter's foundations are strengthened by the NCERT Solutions for Class 10 Mathematical Chapter 9, Some Applications of Trigonometry, Exercise 9.1. These solutions are available in free pdf format. It aids students in reviewing all of the accessible chapter-by-chapter exercise solutions. The extensive explanations provided in the NCERT answers for class 10 math are helpful for students who need to review the material.
The NCERT answers are written by subject experts in mathematics and provide the proper visual representations to help students do better in the first and second semester exams. The CBSE board's norms and freshly revised syllabus are followed in the creation of the NCERT answers.
NCERT Solutions assist students in solidifying their knowledge in circle-related areas.
Diagrams are used to answer questions, making learning more dynamic and thorough.
The language used in NCERT Solutions is simple and easy to grasp.
Students benefit from a step-by-step approach to problem-solving.
Allows learners to work through challenging problems in their own time.
NCERT Solutions for various courses and disciplines are also available for students to use. Our well-experienced professors create these answers to offer clarity on essential ideas and problem-solving abilities.
Students can also obtain a firm grasp of critical topics by referring to additional study resources available in our CBSE Class 10 books.
This chapter may take some time to complete, and students must pay close attention. The NCERT Exemplar for Class 10 Maths is provided here to assist students in solving chapter concerns and obtaining proper answers to complex questions.
The NCERT exemplar-based questions of Chapter 9 for Class 10 Maths, Some Applications to Trigonometry, is an essential study resource for Class 10 students. These assist students in comprehending or solving the sorts of problems that a paper setter asked in the CBSE 2025 examinations of CBSE Class 10 Maths. Furthermore, offering solutions to all applications to trigonometry assists students in effectively preparing for the CBSE 2025 examinations.
The subject matter experts make sure that the errors in the NCERT textbooks are resolved according to the NCERT rules and syllabus.
The NCERT exemplar of Chapter 9 for Grade 10 Maths is accessible at our website. These solutions will assist students in acing their 2025 examinations by preparing for the examinations ahead of time. Students may clarify all of their conceptual questions or doubts with the assistance of the notes of Maths NCERT Solutions for Class 10 of this chapter which OSWAAL provides. Experts have created these NCERT Solutions based on the most recent update to the CBSE syllabus for 2024-25 to help students in Class 10 prepare well for their CBSE 2025 examinations.
OSWAAL's subject matter specialists have created solutions for each question based on the CBSE syllabus (2024-25).
Exercise 9.1 in Class 10 helps students remember how to use a trigonometric function to estimate an object's height and distance without actually measuring it. The real measurement may be carried out by employing the sine, cosine, and tangent functions and certain crucial phrases such
- line of vision
- The elevation angle
- Depression Line
- Horizontal line
These words plus the trigonometric functions make it simple to calculate an object's height and distance. You can quickly determine which trigonometric functions should be utilized to solve a problem once you learn how to determine the angle of elevation and angle of depression for an issue.
Understanding how trigonometry is used in everyday life can help you succeed in the second-term examinations. Learn the whole NCERT answers for class 10 math chapter 9.
Frequently Asked Questions (FAQs) about NCERT Exemplar Solutions for Class 10 Maths Chapter 9:
How many problems are present in each NCERT Exemplar Solutions for Class 10 Maths Chapter 9 exercise?
Answer: Exercise 9.1 contains 16 questions which are of long answer type. Every problem is addressed with the utmost attention to give students accurate solutions following CBSE norms.
Where can I get online NCERT Exemplar Solutions for Class 10 Maths Chapter 9?
Answer: Yes, the NCERT Exemplar Solutions for Class 10 Maths Chapter 9 are available on our website. Subject specialists evaluate the solutions to all problems to give students the most significant reference material. You can download chapter-by-chapter or exercise-by-exercise answers to understand better the problem-solving approaches used while solving textbook questions.
What are the uses of studying Chapter 9 of the NCERT Exemplar for Class 10 Math?
Answer: Finding the height and distance of various objects without measuring is an application of studying NCERT Exemplar for Class 10 Maths Chapter 9. Students who master these ideas will be able to respond to any trigonometry-based questions, and they may also find it easier to complete class assignments and write CBSE Term II examinations.
Is Chapter 9 of the NCERT Exemplar for Class 10 Math sufficient for the CBSE second term exams?
Answer: Yes, you must thoroughly study all of the questions and practise them often. Once you have completed all of the questions, you can consult additional reference materials and the NCERT Exemplar textbooks' questions.
