Welcome to Future Study Point, your trusted resource for easy-to-understand and exam-oriented Class 10 NCERT Solutions based on the CBSE syllabus. In this post, you will find Class 10 Maths NCERT Solutions Chapter 9 – Applications of Trigonometry, with step-by-step explanations to help students understand the concepts and solve questions confidently.
Class 10 Maths NCERT Solution are extremely important for CBSE Board Exam preparation because the NCERT textbook forms the foundation of the CBSE Mathematics syllabus. Solving NCERT questions with step-by-step solutions helps students understand concepts, learn the correct methods, and improve their problem-solving skills.
Regular practice of NCERT exercises also helps students become familiar with important formulas, theorem-based questions, application problems, and exam-style calculations. It builds confidence and helps students write accurate, well-organised solutions in the board examination.
Class 10 Maths Chapter 9 – Applications of Trigonometry
Chapter: 9 – Applications of Trigonometry
Class: 10
Subject: Mathematics
Book: NCERT Mathematics
Board: CBSE
Academic Session: 2026–27
The chapter Applications of Trigonometry shows how trigonometric ratios can be used to solve practical problems involving the height and distance of objects. Students learn how to use angles of elevation and depression along with trigonometric ratios to calculate unknown heights and distances.
Why Are Class 10 Maths NCERT Solutions Important?
Class 10 Maths NCERT Solutions are important for students because NCERT questions help develop the fundamental concepts and problem-solving skills required for CBSE Mathematics. Step-by-step solutions help students understand how to identify the given information, select the appropriate trigonometric ratio, form the required equation and obtain the final answer.
Regular practice of Class 10 Maths NCERT Solutions can help students:
- Understand concepts clearly.
- Learn the correct method of solving numerical problems.
- Improve mathematical accuracy.
- Practise important NCERT questions.
- Develop confidence in trigonometry.
- Prepare effectively for CBSE examinations.
- Revise important formulas and concepts quickly.
Topics Covered in Applications of Trigonometry
The important concepts covered in this chapter include:
- Applications of trigonometric ratios.
- Heights and distances.
- Line of sight.
- Angle of elevation.
- Angle of depression.
- Solving practical problems using right-angled triangles.
- Finding the height of an object.
- Finding the distance between objects.
- Using sine, cosine and tangent in real-life situations.
What Are Heights and Distances?
In many practical situations, it is difficult to measure a height or distance directly. For example, we may want to find the height of a tower, building, tree or pole without physically measuring it.
Trigonometry provides a convenient method for finding such unknown quantities by using a known distance and an angle.
A right-angled triangle can be formed between the observer, the object and the ground. Once the appropriate trigonometric ratio is identified, the unknown height or distance can be calculated.
Angle of Elevation
The angle of elevation is the angle formed between the horizontal line through the observer’s eye and the line of sight when the object being observed is above the observer.
For example, when a person looks upward at the top of a tower, the angle between the horizontal line and the line of sight to the top of the tower is called the angle of elevation.
Angle of Depression
The angle of depression is the angle formed between the horizontal line through the observer’s eye and the line of sight when the object being observed is below the observer.
For example, when a person standing on the top of a building looks down at a car on the road, the angle between the horizontal line and the downward line of sight is called the angle of depression.
Important Trigonometric Ratios
For an acute angle θ in a right-angled triangle:
sin θ = Perpendicular / Hypotenuse
cos θ = Base / Hypotenuse
tan θ = Perpendicular / Base
In many questions involving heights and distances, tan θ is particularly useful because it directly relates the perpendicular height and the base distance.
How to Solve Questions from Chapter 9
Follow these steps while solving numerical problems:
Step 1: Read the question carefully
Identify the object whose height or distance has to be calculated.
Step 2: Draw a diagram
Represent the situation using a simple right-angled triangle. Mark the known height, distance and angle.
Step 3: Identify the angle
Determine whether the question involves an angle of elevation or an angle of depression.
Step 4: Select the appropriate trigonometric ratio
Choose sin, cos or tan according to the sides involved.
Step 5: Form the equation
Substitute the known values into the appropriate trigonometric ratio.
Step 6: Simplify
Solve the equation carefully and write the answer with the correct unit.
Example of Application of Trigonometry
Suppose a person stands at a known distance from a tower and observes the top of the tower at an angle of elevation θ.
If the horizontal distance from the person to the tower is d and the height of the tower is h, then:
tan θ = h/d
Therefore,
h = d tan θ
This simple relationship is used in many problems involving heights and distances.
Important Points to Remember
While solving questions from Class 10 Maths Chapter 9 Applications of Trigonometry, remember:
- Always draw a neat diagram.
- Mark the right angle clearly.
- Identify the angle of elevation or depression correctly.
- Check which sides are given and which side is required.
- Select the appropriate trigonometric ratio.
- Use the standard values of trigonometric ratios carefully.
- Write the final answer with the correct unit.
- Do not skip important steps in board-exam solutions.
Class 10 Maths Chapter 9 NCERT Solutions
At Future Study Point, we provide easy and step-by-step Class 10 Maths NCERT Solutions to help students understand every question clearly. Our solutions focus not only on obtaining the final answer but also on explaining the method used to solve the problem.
Students can use these Class 10 Maths Chapter 9 NCERT Solutions for homework, revision, exam preparation and practice.
Frequently Asked Questions
What is Chapter 9 of Class 10 Maths?
Chapter 9 is Applications of Trigonometry.
What is the main concept of Chapter 9?
The main focus of the chapter is applying trigonometric ratios to practical problems involving heights and distances.
What is an angle of elevation?
The angle formed between the horizontal line and the line of sight when an object is above the observer is called the angle of elevation.
What is an angle of depression?
The angle formed between the horizontal line and the line of sight when an object is below the observer is called the angle of depression.
Which trigonometric ratio is commonly used in heights and distances?
The ratio tan θ is commonly used when the height and horizontal distance are involved, although sin and cos may also be required depending on the given information.
Preparation Tips for Chapter 9
To prepare this chapter effectively:
- Revise the six trigonometric ratios.
- Memorise the standard values of 0°, 30°, 45°, 60° and 90°.
- Practise drawing diagrams.
- Understand the difference between elevation and depression.
- Practise all NCERT examples and exercise questions.
- Pay attention to units such as metres and centimetres.
- Practise numerical questions without looking at the solution.
- Revise important questions before the examination.
Conclusion
Class 10 Maths Chapter 9 – Applications of Trigonometry is an important chapter that demonstrates how mathematics can be applied to real-life situations. By understanding angles of elevation, angles of depression, heights and distances, students can solve a wide range of practical problems using trigonometric ratios.
Practising Class 10 Maths NCERT Solutions Chapter 9 regularly will help students strengthen their concepts, improve problem-solving skills and prepare confidently for the CBSE Class 10 Maths examination.
For more Class 10 NCERT Solutions, Maths chapter-wise solutions, important questions, sample papers and CBSE exam preparation, keep visiting Future Study Point.
Class 10 Maths NCERT Solutions CBSE 2026-27 Update
Continue your Class 10 Maths preparation with these useful resources from Future Study Point:
Class 10 Maths Chapter 1 – Real Numbers: Complete NCERT Exercise-Wise Video Solutions
Class 10 Maths Chapter 2 – Polynomials: Complete NCERT Solutions for Polynomials
Class 10 Maths Chapter 3 – Pair of Linear Equations in Two Variables: Complete NCERT Solutions
Class 10 Maths Chapter 4 Quadratic Equations: – Quadratic Equations complete NCERT video solutions
Class 10 Maths Chapter 5 Arithmetic Progression: Arithmetic Progression: complete video solution
Class 10 Maths Chapter 8 Introduction to Trigonometry-Introduction to Trigonometry Video Solutions
Class 10 Maths Basic Sample Paper Solution: Practise with the Complete CBSE Basic Sample Paper Solution
👉 Explore these resources to strengthen your concepts, revise important topics, and prepare effectively for the CBSE Class 10 Maths Board Examination 2026–27.
