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Class 10 Mathematics Revision Notes for Some Applications of Trigonometry of Chapter 9
Mathematics has seeped into every human’s daily life, whether a student or an employee. Focusing on setting the foundation of mathematics, it is necessary for every student to prioritise clearing the basic concepts of the subject. Extramarks has carefully developed Chapter 9 Mathematics Class 10 notes to make the job easier for you. Trigonometry is regarded as one of the crucial topics in the subject of mathematics. The subject remains incomplete if one does not cover the topic of trigonometry. This makes the chapter important for scoring well in the 10th board examinations. Focusing on all the essential questions, the Class 10 Mathematics Chapter 9 Notes will help you develop a firm grip on Chapter 9, Some Applications of Trigonometry. These notes are designed by following the latest CBSE Syllabus and NCERT Books.
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Access Class 10 Mathematics Chapter 9 – Applications of Trigonometry
Introduction
Students will learn about various applications of trigonometry in the world around them in this chapter. One of the oldest disciplines still being studied by academics today is trigonometry. Since the development of trigonometry, astronomers have used it, for example, to determine how far away the planets and stars are from Earth. Additionally employed in geography and navigation is trigonometry. Building maps and figuring out where an island is, concerning its longitude and latitude, involves trigonometry expertise.
Angles of Elevation and Depression:
The angle of elevation
Before diving into the angle of elevation, let’s understand what line of sight is. The line of sight is a straight line drawn from the level of an observer’s eye to the point where it is being observed.
The angle of elevation is the point discovered above the horizontal level, where the angle created by the line of sight with the horizontal is spotted. This angle is named the angle of elevation. From the given figure, let O and P be two points, where P is at a greater level. Suppose that OA and PB are two horizontal lines passing through the points O and P, respectively.
Suppose the observer is at point O and the object is at point P. In that case, the line OP is the line of sight for point P. Angle AOP is situated between the line of sight. The OA (horizontal line) is called the angle of elevation of point P when seen from O.
The angle of depression
The angle formed by the line of sight along with the horizontal when the point is found below the horizontal level is called the angle of depression of any point on the object that is being viewed. The angle BPO is called the angle of depression of the point O as observed from P if the observer is at point P and the object is at point O. The figure makes it clear that the angle of elevation of P when observed from O is equivalent to the angle of depression of O when observed from P.
Solved examples
The angle of elevation of the top of a tower from a point on the ground, which is at a distance of 30 m from the foot of the building, is 30°. Determine the height of the tower.
Suppose AB is the tower’s height and C is the point of elevation, which is at a distance of 30 m from the foot of the building.
In right ⊿ ABC
tan 30° = AB/BC
1/√3 = AB/30
⇒ AB = 10√3
Hence, the height of the tower is 10√3 m.
2. A kite flies at a height of 60 m above the level of the ground. Its string is temporarily tied to a point on the ground. The string’s inclination with the land is at 60°. Determine the length of this string, considering that the string doesn’t have any slack.
Solution:
Inferring from the figure, BC is the height of the kite from the ground is 60 m, AC is the inclined length of the string from the base, and A is the point where the kite’s string is tied.
From the figure drawn,
sin 60° = BC/AC
⇒ √3/2 = 60/AC
⇒ AC = 40√3 m
Hence, the string length from the ground is 40√3 m.
Class 10 Mathematics Chapter 9 Revision Notes
Trigonometry is one of the most essential branches of Mathematics. Students should study all the topics of Class 10 Chapter 9 properly to score well in the examination. Extramarks recommends that students can refer to the notes provided on their website which is as per the latest CBSE syllabus. As exams are getting difficult year by year, it is very essential for students to keep revising all the chapters regularly. Extramarks is a onestop platform where students will get endtoend study material such as important questions, previous years’ question papers, answer keys, etc…
Class 10 Mathematics Notes of Some Applications of Trigonometry
This chapter will enable you to learn the application of trigonometric concepts of triangles, dealing with trigonometric ratios, sides, and angles, angle of depression, and elevation, to name a few. By paying attention to various trigonometric formulas and understanding concepts, you can master the art of solving complex questions. Here are the Class 10 mathematics notes; Chapter 9 will be discussed in detail. But first, let us focus on the multiple benefits you will gain from the notes.
Benefits of Revision Notes Class 10 Mathematics Chapter 9
 The revision notes of class 10 Mathematics chapter 9 have been carefully designed in such a way that every student can dive into the conceptual aspect of the chapter with minimal effort in a short period. Furthermore, the main goal is not to miss out on any crucial concept regarding the chapter.
 This will benefit students in various ways, such as enhancing problemsolving and concentration skills. Therefore, the best suggestion is to practice and revise the notes regularly.
 These CBSE revision notes will help you quickly cover NCERT books along with CBSE additional questions. The Applications of Trigonometry chapter is regarded as one of the most challenging chapters of class 10. These revision notes will guide you through it efficiently.
 These notes are highly illustrative and descriptive in the best way possible. Various aspects such as the exam pattern, vital concepts, and many more are emphasized and highlighted time and time again.
 The revision of formulas and concepts is made easy this way so that students can solve the CBSE sample questions effortlessly. This will make lastminute preparation convenient for them.
 The hectic task of running through several pages of the book before your exam will not be required as Class 10 Mathematics Chapter 9 Notes will help you revise everything in one go.
 It might seem timeconsuming to prepare notes for each chapter, but it is a highly essential practice. Class 10 Mathematics Chapter 9 Notes will help you save timemaking notes and further help you master the concepts.
General Tips
Make sure you go through each pointer and concept concerning Chapter 9 carefully. Keep revising the revision notes as it is necessary to revise to gain a robust understanding repeatedly.
Give first preference to solving various types of problems from the chapter as it is necessary to gain experience solving multiple issues. Never neglect the importance of drawing diagrams because they are the only way you can solve your problem quickly.
Do not forget to revise the notes of Chapter 8, i.e., Introduction to Trigonometry, as a few of the basic concepts of this topic are applied directly in Chapter 9, i.e. Some Applications of Trigonometry.
Revision of the theorems of trigonometry periodically is highly necessary as these concepts will also come in handy in higher classes if you choose to opt for the science stream.
Conclusion
Therefore, one can say that one of the introductory chapters of class 10, chapter 9, is from where a significant set of questions are set every year in CBSE class 10 board examinations. Extramarks will efficiently help you revise this chapter’s crucial topics for your perfect lastminute preparation. The notes are tailored based on the previous years’ question papers such that they can cover every integral part of the chapter. Extramarks has designed these notes comprehensively so that your time can be saved, and the road to scoring a definitive score can be made accessible.
FAQs (Frequently Asked Questions)
1. How can I increase my pace for mathematics preparation to excel in Class 10 Board exams?
The Mathematics exam of the class 10 board exam is highly standardised. It strictly follows the format of the syllabus. This will help you gain robust subjectmatter knowledge by focusing on various topics. You can boost your preparation by emphasising NCERT’s books and others as well. The class 10 chapter 9 notes will help you in revising last minute and secure good marks.
2. What are the benefits of revision notes in Class 10 Mathematics Chapter 9?
Revision notes of any chapter are essential as they will give you a crisp outlook of the integral portions of each chapter. As mentioned above, Some Applications of Trigonometry is one of the trickiest chapters requiring extensive practice to gain expertise. Therefore, it is vital to have access to goodquality revision notes so that you can have the essential points in handy.
3. What do you mean by the line of sight and angle of elevation?
The line of sight is known as the virtual or imaginary line drawn from the eye level of an observer to the point where the object is viewed. On the other hand, the angle of elevation is known as the angle formed between the line of sight and the horizontal line, where the object lies above the horizontal line
4. What do you mean by the angle of depression?
The angle of depression is known as the angle produced when the line of sight and the horizontal line align, where the object can be further viewed above as well as below the horizontal line. This means that we are looking in a downward direction when it comes to the angle of depression.