TEACHGYAN • CLASS 10 MATHEMATICS • NCERT 2026–27

Chapter 9: Some Applications of Trigonometry

Detailed Notes • Worked Examples • Competency • Board Practice

📖 Chapter Explanation

Heights and distances use trigonometric ratios to model real situations. The chapter introduces line of sight, angle of elevation and angle of depression and emphasises careful diagram construction.

🧭 Concept Journey

situation → line-of-sight diagram → angle → choose ratio → solve → interpret

📌 Core Concepts

If an observer looks upward at an object, the angle between the horizontal and line of sight is the angle of elevation. A clear right-triangle diagram prevents many errors.

💡 Worked Example

If an observer looks upward at an object, the angle between the horizontal and line of sight is the angle of elevation. A clear right-triangle diagram prevents many errors.

⚠️ Common Errors

If tanθ=height/distance, then height=distance×tanθ. The correct ratio depends on the known and unknown sides.

🧠 Concept-Based MCQs

A student observes the top of a school building from a known distance. Explain how to draw the diagram and determine the building height from an angle of elevation.

Answer Key: 1-B, 2-C, 3-B, 4-A.

📊 Case-Based / Competency

The observer’s eye level must be considered when the question gives an actual height above ground. Also distinguish elevation from depression.

Draw or identify the mathematical model.
Select the relevant theorem/formula.
Solve with complete working.
Interpret and verify the answer.

🔎 Extension Case

Angle of elevation is measured from: A) vertical line B) horizontal line C) ground only at 90° D) building wall|If opposite and adjacent sides are known, use: A) sin B) cos C) tan D) sec only|A line of sight is: A) the observer’s horizontal line B) the visual line from observer to object C) the vertical height D) the ground line|Angle of depression is measured: A) downward from the horizontal B) upward from vertical C) from the ground only D) from the object only

🔥 HOTS & Board Challenge

Explain why the chosen method works.
Create a similar problem and solve it.
Find and correct a plausible incorrect solution.
Apply the concept to a new context.

✍️ Exam Practice

Define the central concept.
Solve a direct application problem.
Solve a multi-step competency problem.
Interpret a diagram/context.
Write a 5-mark solution with reasoning.

📄 Practice Worksheet

5 concept checks
5 standard problems
3 applications
2 case-based questions
2 HOTS questions
1 board challenge

🎯 One-Minute Revision