Class 10 Math App. of Trigonometry Notes 2025 & Study Material PDF

Have you ever wondered how tall a building is without climbing it? Or how do ships find their way using angles and distance? What if you could measure the height of a mountain without even going near it?

These real-life questions might seem tricky, but the answer lies in a fascinating branch of mathematics—trigonometry. In Chapter 8: Some Applications of Trigonometry, CBSE Class 10 students are introduced to how trigonometry is used outside textbooks, in everyday situations and in professional fields like architecture, navigation, and engineering.

This chapter uses right-angled triangles to focus on practical problems involving heights and distances. You’ll learn how angles of elevation and depression help us solve problems that appear complicated at first, but become simple with the right approach.

Whether you're preparing for your board exams or just want to understand the usefulness of maths in the real world, this chapter gives you a solid foundation. Let’s explore the important concepts, formulas, and examples that make trigonometry important and exciting too!

CBSE Class X Some Applications of Trigonometry Notes

Class 10 Some Applications of Trigonometry chapter 9  notes cover all the main concepts like the measurement of heights and distances, navigation, and many others. The downloadable notes PDFs for Applications of Trigonometry are provided below in detailed and easy-to-understand language.

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Chapter 8 Some Applications of Trigonometry: Important Notes

This chapter focuses on the practical use of trigonometry to find heights and distances. It is based on right-angled triangles and uses trigonometric ratios like sine, cosine, and tangent to solve problems.

Important Terms to Remember

• Line of Sight: The straight line from the observer’s eye to the object being viewed.
• Angle of Elevation: The angle formed when the object being viewed is above the horizontal level of the observer.
• Angle of Depression: The angle formed when the object being viewed is below the horizontal level of the observer.

Important Trigonometric Ratios (For a Right-Angled Triangle)

These are based on the angle inside the triangle:

• sin θ = Opposite / Hypotenuse
• cos θ = Adjacent / Hypotenuse
• tan θ = Opposite / Adjacent

In this chapter, you mostly use these three ratios: sin, cos, and tan.

Things to Keep in Mind While Solving Problems

• Always draw a diagram to understand the situation.
• Label the triangle properly with the given data.
• Identify which trigonometric ratio fits the problem (based on what is given and what is required).
• Make sure the angles are taken from the correct position (elevation or depression).
• Use proper units (metres, kilometres, etc.) and make conversions if necessary.

Real-Life Applications of Trigonometry

• Finding the height of a tower or tree.
• Measuring the distance between two objects.
• Navigation and locating ships or aeroplanes.
• Architecture and construction work.
• Solve the equation step-by-step to avoid mistakes.

No Need to Memorise Too Much

This chapter doesn't ask you to learn new formulas; instead, it teaches you how to apply existing trigonometric knowledge in practical ways. It's more about understanding the situation and choosing the right approach.

CBSE Class X Some Applications of Trigonometry: Important Formula

Understanding trigonometry becomes much simpler when you’re clear on the formulas. This chapter doesn’t introduce any new trigonometric formulas, but it focuses on applying the ones you already know from earlier chapters to solve real-world problems related to heights and distances.

Below is a list of the important trigonometric formulas you’ll use in this chapter:

Basic Trigonometric Ratios (For a Right-Angled Triangle)

If θ is one of the angles in a right-angled triangle:

• sin θ = Opposite Side / Hypotenuse
• cos θ = Adjacent Side / Hypotenuse
• tan θ = Opposite Side / Adjacent Side
• cot θ = 1 / tan θ = Adjacent / Opposite
• sec θ = 1 / cos θ = Hypotenuse / Adjacent
• cosec θ = 1 / sin θ = Hypotenuse / Opposite

These ratios are used to relate the sides of a triangle to its angles.

Important Relationships to Remember

You mostly need these three ratios in this chapter:

• tan θ = sin θ / cos θ
• cot θ = 1 / tan θ
• tan²θ + 1 = sec²θ
• cot²θ + 1 = cosec²θ

Height and Distance Formula Applications

There are no separate "height and distance" formulas. Instead, you use the trigonometric ratios in real-life situations.

For example:

• To find the height of an object, use:

tan θ = Height / Distance from the object

• To find the distance from the object, use:

Distance = Height/tan θ

Just rearrange the formula depending on what you need to find.

Angle of Elevation and Depression

• Use tan θ when you're dealing with vertical height and horizontal distance.
• Always draw a diagram to figure out where to apply the correct formula.
• Remember:
  
  • Angle of Elevation – when you look up at an object.
  • Angle of Depression – when you look down at an object.

CBSE Class X Some Applications of Trigonometry: Useful Tips for Exams

Struggling to remember how to use trigonometry in real-life problems? Confused about angles of elevation and depression? Don’t worry—these simple exam tips will help you master Chapter 8 and boost your Maths marks!

Here are some practical and student-friendly tips to score well in this chapter:

Understand, Don’t Memorise

This chapter is not about learning new formulas—it’s about applying what you already know. Focus on understanding how to use sine, cosine, and tangent to solve height and distance problems.

Always Draw a Clear Diagram

A neat, labelled diagram is half the battle won. It helps you:

• Visualise the situation
• Identify right-angled triangles
• Place angles and sides correctly (especially elevation or depression)

Read the Question Carefully

Check for these important points:

• Is it an angle of elevation (looking up) or angle of depression (looking down)?
• What is being asked—height, distance, or angle?
• Are units given in metres or kilometres?

Label the Triangle Correctly

In your triangle:

• Hypotenuse is always opposite the right angle.
• Opposite side is across from the angle you’re working with.
• Adjacent side is next to the angle.

Knowing which side is which helps you choose the right trigonometric ratio

Choose the Correct Ratio

Use:

• tan θ = Opposite / Adjacent (most commonly used in this chapter)
• sin θ = Opposite / Hypotenuse
• cos θ = Adjacent / Hypotenuse

Pick the one based on what information you are given.

Practice with Real-Life Examples

The more you practice, the faster you’ll get. Solve questions from:

• NCERT textbook
• Previous years’ question papers
• Sample papers

Why Download These Chapter-wise PDFs?

For courses like Mathematics, including Ch 9 class 10 MathSome Applications of Trigonometry, downloading chapter-specific PDFs can have the following benefits:

• Chapter-specific studying using PDFs is arranged and structured. It is simpler for students to efficiently organize their study time when they can concentrate on particular topics or chapters.
• Collaborative learning is encouraged when students discuss the PDFs with their instructors or fellow students. This is particularly helpful while studying in groups or when looking for help from others.
• PDFs may be accessible offline after they have been downloaded, enabling students to continue their studies even in the absence of an internet connection. Students who only sometimes have regular access to the web will find this very useful.
• PDFs are lightweight and compatible with many different devices. This mobility encourages flexibility in learning plans by allowing students to study Chapter 8 on Arithmetic Progression whenever and wherever they want.
• Chapter-wise revision and review are made possible by PDFs. Before tests, students may review particular chapters or subjects to assist in solidifying their learning.

How Can This Chapter-wise Material Help Students?

For a structured and methodical approach to understanding concepts in mathematics, chapter-wise study materials for class X Some Applications of Trigonometry are essential. It facilitates focused practice, efficient review, and the building of a solid conceptual basis, all of which lead to a deeper comprehension of the topic. After downloading chapter notes, DoE worksheets, question banks, and many other study materials, students can prepare for the chapter effectively.

• Having chapter-wise Some Applications of Trigonometry class 10 notes helps with an effective review when tests get near. Students can focus on particular areas that require more attention, resulting in a review that is more focused and efficient.
• Mind maps are useful memory supports because of their visual and hierarchical format. If students mentally follow the branches and links inside the mind map, they will be able to recall knowledge more quickly.
• Most question banks include every topic in the curriculum. By selecting questions according to the subjects they choose to concentrate on, students may create a personalized and flexible study schedule.
• The repeated patterns and trends in earlier question papers are usually taken into account while selecting important questions. Students get acquainted with the kinds of questions that will probably be on the test by practicing these questions.
• Experiential learning helps close the gap between mathematical concepts and practical applications. The topic becomes more relevant and useful when students learn how mathematical ideas are applied in a variety of industries, including science, engineering, finance, and technology.

Common Mistakes Students Make in CBSE Class X Some Applications of Trigonometry

Are you losing marks in this chapter even though you know the formulas? You’re not alone. Many Class 10 students make simple yet common mistakes in Chapter 8 – Some Applications of Trigonometry, which can easily be avoided with a little attention and practice.

Here’s a list of the most frequent errors students make—and how to avoid them.

Confusing Angle of Elevation and Depression

Many students mix up these two terms:

• Angle of Elevation is when you look upwards at an object.
• Angle of Depression is when you look downwards from a height.

Tip: Always draw a diagram. It makes it easier to identify the angle correctly.

Not Drawing the Diagram Properly

Some students skip the diagram or draw it incorrectly. This leads to confusion and wrong calculations.

Tip: Always draw a clear, labelled diagram based on the question. It helps you understand the situation better and apply the correct trigonometric ratio.

Using the Wrong Trigonometric Ratio

Choosing the wrong ratio like sin instead of tan, or cos instead of sin, is a very common error.

Tip: Identify the sides in relation to the given angle—opposite, adjacent, and hypotenuse—before choosing the ratio.

Incorrect Labelling of Triangle Sides

Mislabeling the triangle sides often leads to applying the wrong formula.

Tip: Remember:

• Opposite is across from the angle.
• Adjacent is next to the angle (but not the hypotenuse).
• Hypotenuse is always the longest side, opposite the right angle.

Ignoring Units or Mixing Them Up

Many students forget to convert units (e.g., kilometres to metres), or don’t mention them in their final answer.

Tip: Keep an eye on units while reading the question and always write units in your final answer.

Not Using the Calculator or Tables Correctly

If allowed, using trigonometric tables or calculators wrongly can lead to incorrect answers.

Tip: Double-check values from the table or calculator and make sure your calculator is set to degree mode, not radians.

Leaving the Final Answer Without a Statement

Writing only the number without explaining what it means can cost marks.

Tip: End your answer with a clear sentence like:
“Therefore, the height of the building is 30 metres.”

Not Revising Basic Trigonometric Ratios

Forgetting basic formulas like tan θ = opposite/adjacent can create confusion during exams.

Tip: Regular revision of the six trigonometric ratios and how to apply them will help you feel confident.

Not Checking the Reasonableness of the Answer

Sometimes, students calculate a height that’s too large or small, but don’t realise it.

Tip: Take a moment to ask yourself: Does this answer make sense in real life? If not, go back and check your steps.

By being aware of these common mistakes, you can easily avoid them and improve your accuracy and confidence in solving trigonometry problems.

A major chapter in the CBSE Class 10 Mathematics syllabus is Some Applications of Trigonometry. These questions and additional supplementary resources are available from Educart, enabling teachers to assist students in practicing this kind of questioning extensively. All you need to download these PDFs is a single click and user authentication.