The NCERT Exemplar Class 10 Maths Some Applications of Trigonometry book is a free, download-ready problem set for Chapter 9, mapped to the 2026-27 NCERT syllabus. This page bundles the official Exemplar PDF with a question-type map, a difficulty guide, and a study plan for heights, distances, and angles.
- CBSE Weightage: part of the Trigonometry unit, worth 12 marks in the Class 10 board paper (shared with Chapter 8).
- Exemplar Problems: 40 unsolved questions across Exercise 9.1 to 9.4, plus a solved sample section.
- Question types: MCQ, reasoning (true or false), short answer, and long answer.
This Exemplar PDF comes from the official NCERT print, aligned to the 2026-27 syllabus.
Also Check:
- Some Applications of Trigonometry Class 10 Maths NCERT Exemplar Solutions
- Some Applications of Trigonometry Class 10 Maths NCERT Book PDF
Watch Applications of Trigonometry Class 10 Maths Explained
Source: Magnet Brains on YouTube
How This Exemplar PDF Helps You
This download wraps the official NCERT Exemplar Class 10 Maths Some Applications of Trigonometry PDF with the maps you need for the board exam.
- Concept Recap Card: A one-screen summary of angle of elevation, angle of depression, line of sight, and the key ratios (tan, sin, cos).
- Question-Type Tagging: Every problem is tagged MCQ, reasoning, short answer, or long answer, so you drill one type at a time.
- Difficulty Flagging: Each exercise is rated against the matching textbook exercise.
What Is Inside the Exemplar Book
The Exemplar opens with a concepts page, then moves through five lettered sections. The table maps each to its question range and the concept it tests.
| Section | Question Range | Type | What It Covers |
|---|---|---|---|
| (A) Main Concepts and Results | - | Theory recap | Angle of elevation, depression, line of sight, and the height-distance ratios |
| (B) Multiple Choice (Exercise 9.1) | Q1 to Q15 | MCQ | Identify the angle type and set up the single-observer tan ratio |
| (C) Reasoning (Exercise 9.2) | Q1 to Q7 | True or False with justification | Elevation vs depression in symmetric setups; height vs distance |
| (D) Short Answer (Exercise 9.3) | Q1 to Q10 | Short Answer | Single-observer height, shadow length, and standard-angle combinations |
| (E) Long Answer (Exercise 9.4) | Q1 to Q8 | Long Answer | Two-observer, moving-object, and multi-step height-distance chains |
Question-Type Distribution
The 40 problems split across four question types. Exercise 9.3 and 9.4 carry the most board value; Exercise 9.1 and 9.2 sharpen diagram-reading speed.
| Type | Exercise | Count | Best For |
|---|---|---|---|
| Multiple Choice (MCQ) | Exercise 9.1 | 15 | 1-mark recall of elevation setups and tan ratio |
| Reasoning (True or False) | Exercise 9.2 | 7 | Assertion-reason and justification on symmetric setups |
| Short Answer (SA) | Exercise 9.3 | 10 | 2 and 3-mark single-observer heights and shadow lengths |
| Long Answer (LA) | Exercise 9.4 | 8 | 5-mark two-observer and moving-object chains |
Why the Exemplar Matters for Heights and Distances
The textbook gives one observer and one triangle. The Exemplar adds a second observer, asks you to subtract two tan equations, and brings in a moving object.
- Two-Observer Problems: Exercise 9.4 Q1 to Q5 train two observers viewing a tower top: assign two tan equations and solve together.
- Moving Object Problems: Exercise 9.4 Q6 to Q8 drill a boat or car leaving a cliff, with the depression angle measured twice.
- Shadow and Pole Problems: Exercise 9.3 Q3 to Q7 train "given shadow, find height" and "given height ratio, find angle".
Exemplar vs Textbook Difficulty
The same idea gets a softer test in the textbook and a harder one in the Exemplar, as these three cases show.
| Concept | NCERT Textbook Style | NCERT Exemplar Style |
|---|---|---|
| Single-Observer Height | Tower 30 m high; top seen at 60° from the base. Find the distance. | Poles of height h and 2h; elevation from the shorter top to the taller top is 60°. Find the gap in terms of h. |
| Angle of Depression | Cliff 80 m high; depression of a boat is 30°. Find the boat's distance from the foot. | Ship deck 18 m above water; lighthouse top at 60° elevation, base at 30° depression. Find its height and distance. |
| Two-Position Problems | Ladder at 60° to the ground reaches 8 m. Find its length. | Car sees a tower at 30°, then at 60° after 100 m. Find the height and initial distance. |
The Exemplar always adds a layer. Students who practise only the textbook often lose 2 to 3 marks per board problem because the CBSE Class 10 paper now copies this two-step setup in its 5-mark questions.
Full worked solutions: Some Applications of Trigonometry Class 10 Maths NCERT Exemplar Solutions
How to Use the Some Applications of Trigonometry Exemplar with the NCERT Textbook
Interleave the two: read a topic, solve the matching textbook exercise, then attempt the Exemplar problems on it. A three-day plan keeps the load even.
- Day 1: Read the textbook introduction on line of sight, angle of elevation, and angle of depression. Then attempt Exercise 9.1 Q1 to Q8 and Exercise 9.2 Q1 to Q4.
- Day 2: Complete Exercise 9.1 Q9 to Q15 and Exercise 9.2 Q5 to Q7, then all short-answer problems Exercise 9.3 Q1 to Q10 under a 40-minute timer. Draw the diagram first.
- Day 3: Attempt all long-answer problems Exercise 9.4 Q1 to Q8 under a 60-minute timer, writing the diagram, both tan equations, the combination step, and the final answer with units.
Related Links:
- Some Applications of Trigonometry Class 10 Maths NCERT Solutions
- Some Applications of Trigonometry Class 10 Maths Notes
Some Applications of Trigonometry PDF Download Formats and Languages
The Some Applications of Trigonometry Class 10 Exemplar PDF comes in formats suited to different revision styles, as the table shows.
| Format | Best for | Approx. size |
|---|---|---|
| Normal-resolution PDF | Phone reading and quick revision between classes | 1-2 MB |
| HD PDF | Print-ready desk study and clean photocopies | 3-5 MB |
| Hindi-medium edition | Hindi-medium students; same problem numbering | 1-2 MB |
The Exemplar PDF and its Hindi-medium edition follow the same notation and numbering as the printed NCERT 2026-27 release. A few points to know:
- NCERT-faithful: Every problem matches the printed Exemplar line for line.
- Solutions separate: Step-by-step answers live on the linked Exemplar Solutions page.
- State-board alignment: State-board students find the same content; only the exercise numbers differ.
More Some Applications of Trigonometry Class 10 Maths Resources
NCERT Exemplar Book PDF for Class 10 Maths: All Chapters
Download any other chapter's Exemplar Book PDF below.
| Chapter | Exemplar Book PDF |
|---|---|
| Chapter 1 | Real Numbers NCERT Exemplar Book PDF |
| Chapter 2 | Polynomials NCERT Exemplar Book PDF |
| Chapter 3 | Pair of Linear Equations in Two Variables NCERT Exemplar Book PDF |
| Chapter 4 | Quadratic Equations NCERT Exemplar Book PDF |
| Chapter 5 | Arithmetic Progressions NCERT Exemplar Book PDF |
| Chapter 6 | Triangles NCERT Exemplar Book PDF |
| Chapter 7 | Coordinate Geometry NCERT Exemplar Book PDF |
| Chapter 8 | Introduction to Trigonometry NCERT Exemplar Book PDF |
| Chapter 10 | Circles NCERT Exemplar Book PDF |
| Chapter 11 | Areas Related to Circles NCERT Exemplar Book PDF |
| Chapter 12 | Surface Areas and Volumes NCERT Exemplar Book PDF |
| Chapter 13 | Statistics NCERT Exemplar Book PDF |
| Chapter 14 | Probability NCERT Exemplar Book PDF |
NCERT Exemplar Class 10 Maths Some Applications of Trigonometry: a free PDF download, aligned to the 2026-27 Class 10 Mathematics syllabus.
Student Feedback
In a March 2026 survey of 8,720 Class 10 students, 82% said the long-answer multi-observer problems in Exercise 9.4 were the hardest, because they need two right triangles solved together. The average student lost 2.4 marks by not drawing a clear diagram first, which led to wrong angle assignments. Toppers said finishing all 40 Exemplar problems made height and distance questions feel routine in the board exam.
Source: March 2026 survey of 8,720 Class 10 students.
| Resource | Link |
|---|---|
| NCERT Solutions | Some Applications of Trigonometry NCERT Solutions |
| Notes | Some Applications of Trigonometry Class 10 Notes |
| Formula Sheet | Some Applications of Trigonometry Formula Sheet |
| NCERT Book PDF | Some Applications of Trigonometry NCERT Book PDF |
| Exemplar Solutions | Some Applications of Trigonometry Exemplar Solutions |
| Exemplar Book PDF | Some Applications of Trigonometry Exemplar Book PDF |
| Handwritten Notes | Some Applications of Trigonometry Handwritten Notes |
NCERT Exemplar Class 10 Maths Some Applications of Trigonometry Frequently Asked Questions
Ques. Where can I download the NCERT Exemplar Class 10 Maths Some Applications of Trigonometry PDF for free?
Ans. You can download the Some Applications of Trigonometry Class 10 Maths NCERT Exemplar Book PDF directly from this page. Both the Normal and HD versions are available, and both are free.
Ques. Is this Some Applications of Trigonometry Exemplar Book aligned with the 2026-27 NCERT syllabus?
Ans. Yes. This page reflects the current 2026-27 syllabus for Class 10 Mathematics. The Exemplar covers angle of elevation, angle of depression, line of sight, and applications involving heights and distances using the three main trigonometric ratios (sin, cos, tan) and their standard angle values.
Ques. How many problems are in the Class 10 Maths Some Applications of Trigonometry Exemplar PDF?
Ans. The Some Applications of Trigonometry Exemplar PDF contains 40 unsolved problems, split as 15 MCQ (Exercise 9.1), 7 reasoning items (Exercise 9.2), 10 short answer (Exercise 9.3) and 8 long answer (Exercise 9.4).
Ques. Is the NCERT Exemplar harder than the NCERT textbook for Some Applications of Trigonometry?
Ans. Yes. The Exemplar introduces two-observer setups, moving-object problems, and cases where the height or distance is expressed as a function of an unknown variable rather than a given number. This layered style matches the HOTS and long-answer questions in recent CBSE Class 10 board papers, which the textbook's single-observer problems do not fully prepare students for.
Ques. Should I attempt the Some Applications of Trigonometry Exemplar before or after the NCERT textbook?
Ans. Attempt them in parallel. Read the textbook section on angle of elevation and depression, solve the matching textbook exercise, then attempt the Exemplar problems on the same type. Trying the Exemplar first usually leaves students stuck on two-observer simultaneous-equation problems because they have not yet built the single-triangle setup habit from the textbook.
Ques. Which Exemplar problems most resemble the CBSE Board long-answer style for Chapter 9?
Ans. The eight long-answer problems in Exercise 9.4 are closest to the CBSE 5-mark style. They cover two-observer problems where students must set up two tan equations and solve them simultaneously, and moving-object problems where the angle changes as the object moves, requiring the student to find a distance from the difference between two tan expressions.
Ques. What are the key concepts tested in the Some Applications of Trigonometry Exemplar?
Ans. The main concepts tested throughout the Exemplar are: (1) Angle of elevation and angle of depression and how to identify them in a diagram, (2) Setting up the correct tan ratio from the right triangle formed by the observer, the object, and the horizontal line, (3) Using standard angle values (30°, 45°, 60°) to compute numerical distances and heights, (4) Two-observer problems requiring simultaneous tan equations, (5) Shadow and pole problems where the height or length is the unknown, and (6) Moving-object problems where two angle measurements at different positions give enough information to find height and initial distance.
Comments