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Some Applications of Trigonometry Class 10 Notes CBSE Maths Chapter 9 (Free PDF Download)

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Class 10 Maths Revision Notes for Some Applications of Trigonometry of Chapter 9 - Free PDF Download

Trigonometry is one of the important branches or subdivision of the discipline of Mathematics. The study of this subject is incomplete without covering this topic and that is why it is also included in Class 10 board examinations as well. As we know that, Class 10 Board is one of the crucial steps for any student and all the students want to get good marks in the board examinations and while completing the whole syllabus of this subject, we need revision notes at the end, thus Vedantu is here to help the students with chapter-wise revision notes that will help them in their preparation and final exams as well. In this article, we have brought Class 10 Maths Notes of Some Applications of Trigonometry which is one of the important and scoring chapters of Class 10, and to cover this Important chapter, you will require revision notes and these notes will solve all of your problems. Register Online for Class 10 Science tuition on Vedantu.com to score more marks in the CBSE board examination. Vedantu is a platform that provides free CBSE Solutions (NCERT) and other study materials for students.

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Some Applications of Trigonometry Class 10 Notes CBSE Maths Chapter 9 (Free PDF Download)
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Access Class 10 Maths Chapter 9 - Applications of Trigonometry

Angles of Elevation and Depression:

  • The line of sight is a line drawn from an observer's eye to a point in the thing being observed.

  • Angle of Elevation:

When the point being observed is above the horizontal level, the angle created by the line of sight with the horizontal is called the angle of elevation of the point being viewed.

  • Let $\text{O}$ and $\text{P}$ be two points, with $\text{P}$ being the greater level. Assume that $\text{OA}$ and $\text{PB}$ are horizontal lines that pass through $\text{O}$ and $\text{P}$, respectively.

  • If the observer is at $\text{O}$ and the object is at $\text{P}$, the line $\text{OP}$ is known as the line of sight of Point $\text{P}$, and the angle $\text{AOP}$ between the line of sight and the horizontal line $OA$ is known as the angle of elevation of Point $\text{P}$ as seen from $\text{O}$.


Angles of Elevation and Depression


  • Angle of Depression:

The angle created by the line of sight with the horizontal when the point is below the horizontal level is known as the angle of depression of a point on the object being viewed.

  • The angle $\text{BPO}$ is known as the angle of depression of $\text{O}$ as seen from $\text{P}$ if the observer is at $\text{P}$ and the object under examination is at $\text{O}$.

  • From the diagram, it is obviously clear that the angle of elevation of a point $\text{P}$when viewed from a point $\text{O}$ is equal to the angle of depression of $\text{O}$ when viewed from $\text{P}$.


Example:

1. From the top of a $\text{7 m}$ high building, the angle of elevation of the top of a cable tower is \[\text{6}{{\text{0}}^{\text{0}}}\] and the angle of depression of its foot is \[{{45}^{\text{0}}}\] . Determine the height of the tower.

Ans:


Example of Angles of Elevation and Depression


Given Data:

Given the height of building $\text{= 7 m}$

Angle of the elevation of top of a tower from the top of building \[\text{= 6}{{\text{0}}^{\text{0}}}\]

Angle of the depression of the foot of a tower \[\text{= 4}{{\text{5}}^{\text{0}}}\]

To find:

We need to calculate the height of the tower, that is \[\text{AE}\]

Sol:

From the given data, we have

Angle of elevation, that is 

\[\angle \text{ACB = 6}{{\text{0}}^{\text{0}}}\]

Angle of depression, that is

\[\angle \text{BCE = 4}{{\text{5}}^{\text{0}}}\]

Here,

$BE = CD = 7 m$

In the right angled triangle \[ABC\] ,

\[\text{tan }\!\!\theta\!\!\text{  = }\dfrac{\text{Opposite Side}}{\text{Adjacent Side}}\]

Therefore,

$\text{tan 6}{{\text{0}}^{0}}\text{ = }\dfrac{\text{Opposite Side}}{\text{Adjacent Side}}$ 

$\text{tan 6}{{\text{0}}^{0}}\text{ = }\dfrac{\text{h}}{\text{CB}}$

Thus,

\[\text{h = CB }\!\!\times\!\!\text{ tan 6}{{\text{0}}^{\text{0}}}\]

Since,

\[\text{tan 6}{{\text{0}}^{\text{0}}}=\sqrt{3}\]

Therefore,

$\text{h = CB }\!\!\times\!\!\text{ }\sqrt{\text{3}}$

$\text{h = }\sqrt{\text{3}}\text{ CB          ------}\left( \text{1} \right)$

In the right angled triangle \[CBE\] ,

\[\text{tan }\!\!\theta\!\!\text{  = }\dfrac{\text{Opposite Side}}{\text{Adjacent Side}}\]

Therefore,

$\text{tan 4}{{\text{5}}^{0}}\text{ = }\dfrac{\text{Opposite Side}}{\text{Adjacent Side}}$

$\text{tan 4}{{\text{5}}^{0}}\text{ = }\dfrac{7}{\text{CB}}$

Since,

\[\text{tan 4}{{\text{5}}^{\text{0}}}=1\]

Therefore,

$\text{   7 = CB }\!\!\times\!\!\text{ 1}$

$\text{CB = 7          ------}\left( \text{2} \right)$

By putting the equation \[\left( 2 \right)\] in the equation \[\left( 1 \right)\], we get

$\text{   h = 7 }\!\!\times\!\!\text{ }\sqrt{\text{3}}$

$\text{AB = 7}\sqrt{\text{3}}$

Therefore, total height of the tower can be calculated as,

Total height of the tower,

$\text{AE = AB + BE}$

$\text{AE = 7}\sqrt{3}+7$

$\text{AE = 7}\left( \sqrt{3}+1 \right)$

Therefore, the total height of the tower is \[\text{7}\left( \sqrt{3}+1 \right)\] unit.


Class 10 Maths Chapter 9 Revision Notes

Class 10 Maths Notes of Some Applications of Trigonometry

Trigonometry is a mathematical concept that we apply on angles and sides of triangles and it serves as a very important and scoring topic for the Class 10 syllabus. The chapters and their weightage for Class 10 board exams are mentioned below in the table:

Introduction to Trigonometry

Applications of Trigonometry

Weightage of 12 Marks in Exam


You will learn how to apply trigonometry concepts on triangles, how to deal with trigonometric ratios, angles and sides, angle of elevation, angle of depression, etc. in this chapter. With the help of various trigonometric formulas and concepts, you will be able to solve statement-based questions of this chapter as well. We will cover Class 10 Maths Chapter 9 revision notes in this article and will see the various benefits of these notes:


Benefits of Revision Notes Class 10 Maths Chapter 9

  • Class 10 revision notes Maths Ch 9 are designed in such a way that students will be able to go through all the concepts at once in very little time and they will not miss any important concept related to the chapter.

  • Revision notes of Chapter 9 will benefit the students in a number of ways such as it is going to help them in speeding up the problem-solving skills of the students and for this, we suggest practising and revising these notes regularly.

  • Class 10 Revision Notes Some Applications of Trigonometry will help you in covering the important and scoring topics of the syllabus that is Trigonometry and Chapter 9 is considered as one of the toughest and scoring chapters and these notes will help you in preparing this topic.

  • The Class 10 Revision Notes Maths Ch 9 created and provided by Vedantu are in a very illustrative and descriptive way. While preparing these notes, we have kept every important point in our mind like your exam pattern, important concepts which need to be highlighted, again and again, all the concepts related to Chapter 9 and Trigonometry, etc.

  • With Maths Class 10 Some Applications of Trigonometry Notes, Students will be able to learn and revise all the formulas or concepts even a moment before any exam and this last moment revision will be very beneficial also because it will accelerate their exam preparation and will help you in solving long statement based questions.

  • Notes of Class 10 revision Notes Chapter 9 will be beneficial for you if students build the habit of revising these notes always before they start with problem-solving. The revision notes are designed by experts by keeping in mind the students' need for last-minute revision before attempting any chapter so they can optimize their results.

  • Before any test or exam, you will not have to turn all the pages of the Trigonometry chapter in a book to revise the concepts. Some Applications of Trigonometry Class 10 notes will solve this problem and you will not miss any important point at the end while revisioning.

  • Preparing notes for revision at the end in such a way you take less time in covering any chapter is very time-consuming but important as well and these Class 10 Maths Revision Notes Chapter 9 will help you to save that time and that time you can use actually to practice which is more important to master the concepts.


General Tips

  • While revising, go through every point and concept related to the chapter carefully in Ch 9 Class 10 Maths revision notes because it is one of the toughest chapters of Class 10.

  • Prefer revising it every time before you start solving the problems of the chapters because in these chapters you have to deal with statement-based questions and need to make their diagrams as well, only then you will be able to solve the question at the end.

  • Do also revise the notes of Chapter 8 related to Introduction to Trigonometry because some of the basic concepts of that chapter will also be used in Chapter 9.

  • You can revise it again in future grades before you start with the Trigonometry chapter in upper classes as well.

Solved Questions

1. 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 tower, is 30°. Determine the height of the tower.

Solution:

Let AB be the height of the tower and C be the point of elevation, which is at a distance of 30 m from the foot of the tower.

(Image Will Be Updated Soon)

 

In right ⊿ ABC

tan 30° = AB/BC

1/√3 = AB/30

⇒ AB = 10√3

Therefore, 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 ground is at 60°. Determine the length of this string, considering that the string doesn’t have any slack.

Solution:

Sketch out a figure based on the given information.

(Image Will Be Updated Soon)

From the figure BC = Height of the kite from the ground = 60 m, AC = Inclined length of the string from the ground, and A be the point where the string of the kite is tied.

From the drawn figure,

sin 60° = BC/AC

⇒ √3/2 = 60/AC

⇒ AC = 40√3 m

Therefore, the length of the string from the ground is 40√3 m.


Benefits of Revision Notes Class 10 Maths Chapter 9

  1. Comprehensive Concept Review:

  • Designed for a quick yet comprehensive review of all concepts in Chapter 9.

  • Ensures no crucial topic related to the chapter is missed during revision.


  1. Enhanced Problem-Solving Skills:

  • Benefits students by accelerating problem-solving skills.

  • Regular practice and revision of these notes are recommended for optimal results.


  1. Coverage of Important and Scoring Topics:

  • Focuses on crucial and scoring topics of the syllabus, particularly Trigonometry.

  • Assists in preparing for Chapter 9, considered both challenging and rewarding.


  1. Illustrative and Descriptive Presentation:

  • Vedantu's Revision Notes are illustrative and descriptive, considering exam patterns and highlighting important concepts.

  • Emphasizes key points related to Chapter 9 and Trigonometry for effective learning.


  1. Last-Minute Revision Benefits:

  • Enables last-minute revision with the ability to learn and revise formulas or concepts just before exams.

  • Particularly beneficial for solving lengthy statement-based questions.


  1. Effective Habits for Success:

  • Encourages the habit of revising notes before problem-solving sessions.

  • Expertly designed for last-minute revision, optimizing results for students.


  1. Convenient Revision Process:

  • Eliminates the need to flip through entire Trigonometry chapters before tests.

  • Solves the problem of missing crucial points during revision.


  1. Time-Efficient Preparation:

  • Saves time in preparing comprehensive revision notes for Chapter 9.

  • Allows students to allocate saved time for essential practice sessions, crucial for mastering concepts.


Incorporated in the CBSE Class 10 Maths syllabus, this Trigonometry chapter emphasizes a practical approach, aiding students in mastering its application in daily life and exams. To facilitate easy comprehension, our expert teachers have curated study materials that simplify the topic without unnecessary complexity. We recommend students delve into these revision notes and explore related links in this article to optimize their learning experience and make the most of the valuable insights provided by our experts.


Conclusion:

When it comes to Class 10 Maths, Trigonometry stands out as a crucial and high-scoring topic, comprising two vital chapters. Questions from this area are a recurring feature in exams, emphasizing the need for thorough practice. Vedantu addresses this with Class 10 Maths Notes on Some Applications of Trigonometry, aiding in last-minute revision. Tailored to the syllabus and board exam requirements, these notes save time, allowing students to concentrate on studies. Designed for those aiming for good marks, Vedantu's notes ensure a quick recap without missing any details, empowering students to confidently solve problems from this chapter.


Related Study Materials for Class 10 Maths Chapter 9 Some Applications of Trigonometry


Chapter-wise Links for Mathematics Class 10 Notes


Related Important Links for Mathematics Class 10

Along with this, students can also download additional study materials provided by Vedantu for Maths Class 10–

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FAQs on Some Applications of Trigonometry Class 10 Notes CBSE Maths Chapter 9 (Free PDF Download)

1. What are the key concepts covered in the revision notes for Some Applications of Trigonometry Class 10?

Some Applications of Trigonometry Class 10 revision notes focus on core concepts such as:

  • Line of sight, angle of elevation, and angle of depression
  • Using trigonometric ratios for calculating heights and distances
  • Problem-solving strategies for real-life applications
  • Application of tan, sin, and cos in statement-based questions
Each concept is presented with clear diagrams and examples, supporting quick revision as per CBSE 2025–26 syllabus.

2. How should I revise Some Applications of Trigonometry Class 10 for board exams?

To effectively revise Some Applications of Trigonometry Class 10, follow these steps:

  • Review all key formulas and definitions such as angle of elevation and depression
  • Practice solving at least 4–5 previous year problems daily
  • Refer to concise revision notes before attempting statement-based questions
  • Focus on drawing accurate diagrams for each type of application question
This ensures you cover important points and improve your problem-solving speed for the exam.

3. What are the essential formulas included in the Class 10 Maths Chapter 9 revision notes?

The essential formulas in Class 10 Maths Chapter 9 include:

  • tan θ = Opposite/Adjacent
  • sin θ = Opposite/Hypotenuse
  • cos θ = Adjacent/Hypotenuse
  • Heights and distances problems using trigonometric ratios
Mastery of these formulas is vital for quick and accurate problem-solving in the board exam.

4. How are angles of elevation and depression used in real-life problems as per Class 10 revision notes?

Angles of elevation and depression are practical tools to find unknown heights or distances in real life. According to the revision notes:

  • Angle of elevation helps calculate the height of a tall object when observed from the ground
  • Angle of depression is used when the observer looks downward from a height
  • Both require the use of right triangles and trigonometric ratios to solve
Such skills are frequently applied in exams following the CBSE 2025–26 pattern.

5. What is the typical order of revision recommended for Some Applications of Trigonometry Class 10?

The optimal order of revision is:

  • Begin with definitions: line of sight, angles of elevation and depression
  • Cover trigonometric ratios and their values
  • Move to formula application in simple height/distance problems
  • Advance to mixed and multi-step statement-based questions
  • Finish by revisiting key points and practicing previous year questions
This sequence helps in building conceptual clarity and application skills.

6. Why is Chapter 9 Some Applications of Trigonometry considered a scoring chapter in Class 10 Maths?

Chapter 9 is scoring because:

  • It features standard types of problems, making preparation straightforward
  • Most questions can be solved via formulaic approaches and diagram work
  • Regular practice improves both speed and accuracy
  • The chapter carries significant weightage (12 marks) in CBSE Board exams
Focusing on revision notes gives students an edge in quickly recalling and applying concepts in the exam.

7. How do I avoid common mistakes when solving Class 10 trigonometry application problems?

To avoid common mistakes:

  • Always identify and label right angles correctly in diagrams
  • Assign known and unknown values before calculations
  • Double-check the formula (sin/cos/tan) suitable for each triangle
  • Mind the angle: elevation for upward sight, depression for downward
  • Review units and ensure logical dimensions (e.g., m, km)
Referring to structured revision notes can minimize such errors and enhance accuracy.

8. What is a 'statement-based question' in the context of Some Applications of Trigonometry, and how should I approach it?

A statement-based question describes a real-world scenario (like a tower or kite) and asks for calculation of height, distance, or length. To approach:

  • Carefully read and identify all quantitative data
  • Draw a labelled diagram as per the scenario
  • Select the right trigonometric ratio
  • Formulate the equation and solve step by step
Consistent practice with revision notes and examples is recommended for mastering these problems.

9. What are some frequently misunderstood areas in Class 10 Applications of Trigonometry that I should watch out for?

Frequently misunderstood areas include:

  • The difference between angle of elevation (observer looks up) and depression (observer looks down)
  • Misinterpreting the positioning of observer and object in diagrams
  • Mixing up when to use sin, cos, or tan for a specific triangle
  • Overlooking conversion of units or incorrect labelling
Reviewing concise, expert-prepared revision notes helps clarify these concepts and prevents such errors.

10. How can revision notes help with last-minute preparation for Class 10 Board Maths exams?

Revision notes enable last-minute preparation by:

  • Presenting all formulas, definitions, and key examples in a summarized format
  • Allowing rapid review of important points without reading the entire textbook
  • Boosting confidence through targeted practice right before the exam
  • Supporting a focused approach to commonly tested question types
This time-saving method is ideal for maximizing exam performance in minimal time.

11. What is the 'line of sight' in the context of Class 10 Maths Chapter 9?

The line of sight is the imaginary straight line drawn from the observer’s eye to the object being observed. It forms the basis for calculating angles of elevation and depression in application problems, as per the Class 10 CBSE 2025–26 syllabus.

12. Can you list the key terms every student must remember from Class 10 Some Applications of Trigonometry?

The key terms to remember are:

  • Angle of Elevation
  • Angle of Depression
  • Line of Sight
  • Trigonometric Ratios (sin, cos, tan)
  • Height and Distance
  • Hypotenuse, Opposite, Adjacent sides
These terms are frequently asked in CBSE exams and must be mastered for quick revision.

13. How do angles of elevation and depression relate to the properties of triangles used in Chapter 9?

Both angles of elevation and depression are always associated with right-angled triangles formed in the scenario. The observer, the object, and the horizontal plane together create a triangle, allowing the use of trigonometric ratios to solve for unknown heights or distances. Application of this triangle property is essential for CBSE board exam problems.

14. In what ways can regular revision notes practice help improve problem-solving speed for Class 10 applicants?

Regular practice with revision notes helps by:

  • Familiarizing the student with repeated question formats
  • Ensuring quick recall of formulas and calculation steps
  • Building confidence through exposure to diverse solved examples
  • Developing a habit of drawing and interpreting diagrams efficiently
Consistent use of notes significantly enhances exam readiness and performance.

15. What special advice is given for revision before attempting statement-based questions in Class 10 Maths Chapter 9?

Before attempting statement-based questions in Chapter 9:

  • Revise all definitions and standard formulas
  • Skim through solved examples to recall the logical approach
  • Ensure a clear understanding of diagram construction
  • Double-check units and angle specifications
This approach reduces errors and saves time during the actual exam.