Lesson Plan Math Class 10 (Ch-9) | Applications of Trigonometry
LESSON PLAN, math. CLASS-10
Ch-9, Application of Trigonometry
Rmb dav centnary public school Nawanshahr | |||||
NAME OF THE TEACHER | DINESH KUMAR | ||||
CLASS | X | CHAPTERS | 09 | SUBJECT | MATHEMATICS |
TOPIC | Application of Trigonometry | DURATION : 10 CLASS MEETINGS | |||
PRE-REQUISITE KNOWLEDGE
- Knowledge of Right-Angled Triangles and Pythagorean Theorem.
- Concept of Trigonometric Ratios (sin, cos, tan, cosec, sec, cot) for acute angles.
- Values of trigonometric ratios for standard angles (0°, 30°, 45°, 60°, 90°).
- Basic algebraic simplification and ratio calculations.
TEACHING AIDS
Green Board, Chalk, Duster, Clinometer (angle measuring device), Charts showing trigonometric formulas and right triangle figures, Measuring Tape, Worksheets, Assignments.
TECHNOLOGY REQUIRED
Smart Board, Projector, Laptop, Internet, GeoGebra / Interactive Geometry Software for visual simulation of angles of elevation and depression.
METHODOLOGY
Demonstration, Activity-Based Learning (measuring height of school building/flagpole using clinometer), Lecture Method, and Problem-Solving Technique.
LEARNING OBJECTIVES
- To understand real-world applications of trigonometry in finding heights and distances without actual measurement.
- To define Line of Sight, Horizontal Level, Angle of Elevation, and Angle of Depression.
- To formulate mathematical models and right-angled triangle representations from practical word problems.
- To select and apply appropriate trigonometric ratios to solve heights and distances problems.
After studying this lesson, students will be able to explain and demonstrate:
- Line of Sight, Horizontal Line, Angle of Elevation, and Angle of Depression.
- Drawing accurate diagrammatic representations for real-life situation word problems.
- Calculating heights of objects (buildings, towers, trees) and distances between objects using trigonometric ratios.
- Solving practical multi-step problems involving single and combined right-angled triangles.
- NCERT Text book of Mathematics
- NCERT Exemplar Text Book
- RESOURCE CENTRE at cbsemathematics.com
Line of Sight, Angle of Elevation, Angle of Depression, Horizontal Level, Height, Distance, Trigonometric Ratios, Right Triangle, Clinometer.
CONTENT & PRESENTATION
- Line of Sight and Horizontal Level
- Angle of Elevation
- Angle of Depression
- Applications in calculating Heights and Distances
- Trigonometric Ratio selection for single right-angled triangle
- Trigonometric Ratio selection for combined right-angled triangles
INTRODUCTORY ACTIVITY
Visual observation activity where students look up at a high object (like a ceiling fan, wall clock, or tree top) and note the change in eye level and inclination angle compared to looking straight ahead.
EXPERIENTIAL ACTIVITY
Hands-on measurement of the height of the school flagpole or basketball hoop using a handmade Clinometer (protractor + string + plumb weight) and measuring tape to measure horizontal distance from the base.
ART INTEGRATED ACTIVITY
Students create an illustrated poster or 3D visual diagram mapping real-world structures (towers, lighthouses, kites, airplanes) with clearly marked angles of elevation/depression and corresponding right-angled triangles.
PROCEDURE
Begin the session by explaining why trigonometry was developed historically (astronomy, navigation, surveying, geography). Introduce practical contexts like finding the height of a tall mountain or tree without climbing it.
PRESENTATION OF THE TOPIC
Introduction
- Line of Sight: The line drawn from the eye of an observer to the point in the object viewed by the observer.
- Horizontal Level: The line drawn parallel to the ground from the eye of the observer.
- Angle of Elevation: The angle formed by the line of sight with the horizontal line when the object is ABOVE the horizontal level (i.e. when we look up at an object).
- Angle of Depression: The angle formed by the line of sight with the horizontal line when the object is BELOW the horizontal level (i.e. when we look down at an object). Note: Angle of Depression = Angle of Elevation by alternate interior angles.
Step-by-Step Problem Solving Strategy
Step 1: Read the problem carefully and draw a clear right-angled triangle diagram.
Step 2: Mark given lengths, given angles, and unknown quantities (height 'h' or distance 'd').
Step 3: Identify the right triangle containing the unknown side and known side/angle.
Step 4: Choose the correct trigonometric ratio (usually tan θ = Opposite/Adjacent or sin θ = Opposite/Hypotenuse).
Step 5: Substitute standard trigonometric values (e.g., tan 30° = 1/√3, tan 45° = 1, tan 60° = √3) and solve.
Core Concepts
- Line of Sight
- Horizontal Level
- Angle of Elevation (Looking UP)
- Angle of Depression (Looking DOWN)
Key Ratios Used
- tan θ = Opposite / Adjacent (Height / Distance)
- sin θ = Opposite / Hypotenuse (Height / Slant Distance)
- cos θ = Adjacent / Hypotenuse (Base Distance / Slant Distance)
Application Types
- Single Triangle Problems (Direct height or
distance)
- Dual Triangle Problems (Two observers, moving
objects, multi-level structures)
STUDENTS DELIVERABLES:
- Review questions given by the teacher.
- Students can prepare a Presentation on the topic “prove that given number is irrational number”.
- Solve N.C.E.R.T. problems with examples,
- Solve assignment of Multiple Choice Questions (MCQ) given by the teacher.
EXTENDED LEARNING:-
Students can extend their learning through the RESOURCE CENTRE and can find more valuable and interesting concepts on mathematics at cbsemathematics.com
Students can also extend their leaning by watching this topic on video.
SKILLS ENHANCED
Observation skill, analytical skill, critical & creative thinking, team work, constructive approach, interpersonal skill, engagement in learning process etc.
ASSESSMENT TECHNIQUES:
- Assignment sheet will be given as home work at the end of the topic.
- Separate sheets which will include questions of logical thinking and Higher order thinking skills will be given to the above average students.
- Class Test , Oral Test , worksheet and Assignments. can be made the part of assessment.
- Re-test(s) will be conducted on the basis of the performance of the students in the test.
- Puzzle
- Quiz
- Misconception check
- Peer check
- Students discussion
- Competency Based Assessment link: M C Q
FEEDBACK:
All those students who performed well will be appreciated positively, and all those who can not perform up to the mark will again be given some important tips, guidance and positive motivation to go through the topic again and then re-evaluated again. If possible then provision of remedial classes can be made for batter results.
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