by Tiwari Academy
NCERT Exercise Solutions for Class 10 Mathematics Chapter 9 Some applications of Trigonometry Exercise 9.1 in English and Hindi Medium for CBSE Exams. NCERT Class 10 Maths Textbook Exercise 9.1 Solution explains Height and Distance given in CBSE books of Mathematics published for Session 2024-25. NCERT Textbook Solutions for Class 10 Maths Chapter 9, Some Applications of Trigonometry, are essential for students aiming to excel in their board exams. This chapter primarily deals with practical uses of trigonometry in solving real-world problems like finding the height of a building or the distance of a boat from the shore.
NCERT Exercises Solutions for Class 10 Maths Chapter 9
Students often seek NCERT Class 10 Mathematics Book Chapter 9 solutions PDF to get a clear understanding of the step-by-step methodology for solving these problems. The Class 10 Math Chapter 9 important questions, combined with solved examples, help strengthen the fundamentals of trigonometry. These solutions also highlight how to apply trigonometric ratios to calculate angles and distances efficiently. For additional practice, NCERT Class 10th Textbook Maths Chapter 9 practice questions are a must. Mastering this chapter not only enhances problem-solving skills but also lays the groundwork for advanced studies in mathematics and engineering.
Class 10th Maths Chapter 9 Exercise 9.1 Solutions
NCERT Exercises Class 10 Maths Chapter 9 notes provide a concise overview of key concepts, such as angles of elevation and depression, making it easier for students to revise quickly. The Class 10 Mathematics Chapter 9 formula sheet is another invaluable resource, offering all the necessary formulas in one place to solve application-based problems accurately. Students often rely on the NCERT Class 10th Math Chapter 9 Exercise question answers to understand how theoretical concepts are applied in practical scenarios.
The NCERT complete solutions for Trigonometry applications include detailed explanations of derivations, ensuring that students grasp the underlying principles. By practicing with NCERT 10th Mathematics Chapter 9 solved examples, students can identify common mistakes and improve their accuracy. These resources collectively help students build confidence and prepare for the challenging problems presented in exams.
Important Points in Class 10 Maths Chapter 9 for Board Exams
Angles of Elevation and Depression: Key concepts for solving height and distance problems.
Trigonometric Ratios: Application of sine, cosine and tangent.
Formulae: Memorize height-distance formulas.
Real-Life Problems: Focus on application-based questions.
Steps and Accuracy: Show clear calculations for full marks.
| Day | Topic | Resources | Activities |
|---|---|---|---|
| Day 1 | Introduction to Trigonometry Applications | NCERT textbook, class notes | Read theory, understand angles of elevation/depression |
| Day 2 | Trigonometric Ratios in Real-Life Problems | NCERT solutions, video tutorials | Solve simple problems, focus on ratios |
| Day 3 | Height and Distance Problems | NCERT exercises, practice questions | Solve examples, practice diagrams |
| Day 4 | Advanced Problems | Previous year questions, sample papers | Solve mixed difficulty questions |
| Day 5 | Revision and Doubts | Class notes, NCERT solutions | Review formulas, clear doubts |
| Day 6 | Mock Test | Mock papers, NCERT exercises | Take a timed test, analyze mistakes |
For a deeper understanding of the Applications of Trigonometry, NCERT Class 10 Mathematics Book Trigonometry problems and solutions offer targeted insights into solving advanced questions. Video solutions for Class 10 NCERT Math Exercise Chapter 9 are especially helpful for visual learners, as they demonstrate problem-solving techniques in real-time. Whether it’s calculating the height of a tower or determining the distance between two objects, NCERT Class 10th Maths Textbook Chapter 9 problem-solving techniques are vital for success.
Students should explore Class 10 Math Chapter 9 exercise solutions for comprehensive practice, as these exercises cover a range of difficulty levels. NCERT Grade 10th Mathematics Trigonometry exercises include application-based problems to develop a practical understanding of the topic. With regular practice using these resources, students can effectively prepare for exams and improve their analytical thinking, making this chapter a cornerstone of their mathematical education.
| Class: 10 | Maths |
| Chapter 9: | Some applications of Trigonometry |
| Content Type: | PDF, Text and Videos Format |
| Academic Session: | CBSE Board 2024-25 Exams |
| Medium: | English and Hindi Medium |
Class 10 Maths Chapter 9 Solutions
Class 10 Maths Chapter 9 Question-Answers are updated for new academic session. UP Board also implemented NCERT Books in their curriculum for session 2024-25 onward. So, UP Board Students also take the benefits of these solutions. They can download UP Solutions for Class 10 Maths Chapter 9 from this webpage of Tiwari Academy. NCERT Solutions 2024-25 are available in Video Format also for CBSE Board as well as UP Board students in session 2024-25. Download Offline Apps for the CBSE exams which are based on latest CBSE syllabus 2024-25. If you are facing any difficulty to access the contents of Tiwari Academy website, contact us for help. We will help you as soon as possible.
10th Maths Chapter 9 Solutions
CBSE NCERT Textbook Solutions for class 10 Maths Chapter 9 in English and Hindi Medium available to use online or download in PDF format for offline. Join the discussion forum to ask your doubts and discuss your education queries.
Previous Years Questions
Important Definitions and application on Trigonometry
What is the use of Trigonometry in daily life?
Trigonometry has wide application in solving problems related to real life situations. One of the best methods for the indirect measurement of length or height involve trigonometric rations. Trigonometry is extensively used in geography, navigation, astronomy, etc. The knowledge of trigonometry is used to construct maps, determine the position of different islands in relation to the longitudes and latitudes.
What is horizontal ray?
Horizontal Ray: A ray parallel to the surface of the Earth emerging from the eye of an observer is called a horizontal ray.
What do you understand by Line of Sight?
Line of Sight: The line of sight (or ray of vision) is the line drawn from the eye of an observer to the point in the object viewed by the observer.
What do you mean by Angle of Elevation?
Angle of Elevation: The angle of elevation of the point viewed is the angle formed by the line of sight with the horizontal when the point being viewed is above the horizontal level.
What is Angle of Depression?
Angle of Depression: The angle of depression of a point on the object being viewed is the angle formed by the line of sight with the horizontal when the point is below the horizontal level.
What is line of sight?
The line of sight is the line drawn from the eye of an observer to the point in the object viewed by the observer.
How do you find an angle of elevation?
The angle of elevation of the point viewed is the angle formed by the line of sight with the horizontal when the point being viewed is above the horizontal level.
What is meant by angle of depression?
The angle of depression of a point on the object being viewed is the angle formed by the line of sight with the horizontal when the point is below the horizontal level.
How can we find the height of an object without measuring?
The height or length of an object or the distance between two distant objects can be determined with the help of trigonometric ratios.
ONE MARK QUESTIONS
1. The ratio of the height of a tower and the length of its shadow on the ground is √3:1. What is the angle of elevation of the sun? [CBSE 2017]
THREE MARKS QUESTIONS
1. From the top of a 7 m high building, the angle of elevation of the top of a tower is 60 and the angel of depression of its foot is 45. Find the height of the tower. [CBSE 2017]
FOUR MARKS QUESTIONS
1. Two points A and B are on the same side of a tower and in the same straight line with its base. The angles of depression of these points from the top of the tower are 60 and 45 respectively. If the height of the tower is 15 m, then find the distance between these points. [CBSE 2017]
Historical Facts!
1. Surveyors have used trigonometry for centuries. One such large surveying project (which is used for measuring angles with a rotating telescope) of the nineteenth century was the ‘Great Trigonometric Survey’ of British India for which the two largest-ever theodolites were built.
2. During the survey in 1852, the highest mountain in the world was discovered. From a distance of over 160 km, the peak was observed from six different stations.
3. In 1856, this peak was named after Sir George Everest, who had commissioned and first used the giant theodolites. The theodolites are now on display in the Museum of the Survey of India in Dehradun.
Golden Words
The mathematician does not study mathematics because it is useful. He study it because he delights in it and he delights in it because it is beautiful. … Henri Poincare
What is the importance of NCERT Solutions for Class 10 Maths Chapter 9?
NCERT Complete Solutions for Class 10 Maths Chapter 9, Some Applications of Trigonometry, are crucial for understanding real-world applications of mathematical concepts. They help students solve problems involving angles of elevation and depression, such as calculating the height of a building or the distance between two objects. These solutions provide step-by-step methods, making it easier to grasp the concepts and formulas. They also include solved examples and practice questions that strengthen problem-solving skills. These solutions are aligned with the CBSE syllabus, ensuring students are well-prepared for board exams and competitive assessments.
What should we recall before starting chapter 9 of class 10 Maths?
Before starting chapter 9 Some Applications of Trigonometry of class 10 math students should revise all formulas and identities mentioned in chapter 8 Introduction to Trigonometry of class 10 math. If students remember all formulas and identities mentioned in chapter 8 on tips then chapter 9 becomes easy to understand.
How can I use Class 10 Maths Chapter 9 notes effectively?
The notes for Class 10 Mathematics Chapter 9 summarize key concepts, formulas and methodologies in a concise format, making them ideal for quick revisions. Start by reviewing the Class 10 Maths Chapter 9 formula sheet to familiarize yourself with the essential formulas. Next, go through the theoretical explanations to understand the applications of trigonometry. Practice the solved examples included in the notes, as they demonstrate step-by-step solutions to typical problems. Finally, use the notes to solve NCERT Math exercise questions and test your understanding. Revisiting these notes regularly can help you retain concepts and improve exam performance.
What are the main topic to study in Class 10 Maths NCERT Chapter 9?
In chapter 9 Some Applications of Trigonometry of class 10 math, students will study how trigonometry is used for finding the heights and distances of various objects, without actually measuring them. Also in this chapter students will see the meaning of Angle of Elevation and Angle of Depression.
What resources are available for mastering Class 10 Maths Chapter 9?
Several resources can help students master Class 10 Maths Chapter 9. These include NCERT Mathematics solutions, practice questions and formula sheets. The math solutions guide students through various problem-solving techniques and offer detailed explanations. The NCERT Class 10 Maths Chapter 9 PDF provides easy access to solved examples and exercises. Video solutions are especially helpful for visual learners, showcasing how to approach problems in real time. Practicing with Class 10 Mathematics Chapter 9 important questions prepares students for exam patterns. Regular use of these resources ensures a strong foundation in trigonometry and its applications.
How many exercise are there in chapter 9 of 10th Math?
There is only 1 exercise (Exercise 9.1) having 16 questions and 7 examples in chapter 9 of class 10 math. All the examples and questions of this exercise are good. This chapter needs lot of practice.
How can I improve my problem-solving skills for Chapter 9?
Improving problem-solving skills for Chapter 9 requires regular practice and a structured approach. Start by thoroughly understanding the concepts of angles of elevation and depression. Use the NCERT Class 10 Mathematics Chapter 9 notes to review the key formulas and their applications. Solve NCERT Math exercise questions and practice with additional Class 10 Maths Chapter 9 practice questions. Analyze the solved examples to learn efficient problem-solving methods and avoid common mistakes. Watching video solutions can also provide new perspectives on tackling complex problems. With consistent practice and revision, you can build confidence and excel in this chapter.
What are real life applications of trigonometry in 10th Maths Chapter 9?
Trigonometry is one of the most ancient subjects studied by scholars all over the world. It was invented because its need arose in astronomy. Some real life applications of trigonometry are:
1) To calculate distances from the Earth to the planets and stars.
2) Trigonometry is used in geography and in navigation.
3) The knowledge of trigonometry is used to construct maps, to determine the position of an island in relation to the longitudes and latitudes.
4) To calculate height of buildings, towers and monuments.
