Class: Junior Secondary School 2 (JSS2, JSS 2)
Term: 2nd Term
Week: 10
Age: 13 years
Duration: 45 minutes
Subject: Mathematics
Curriculum Theme: Mathematics
Previous Lesson: Graphs, Solutions of Linear Equations and Real-Life Linear Graphs
Topic: Angles Of Elevation And Depression
subject Matter: Identifying angles of elevation and depression, Distinguishing between angles of elevation and depression, Measuring angles of elevation and depression, Using angles of elevation and depression in calculating distances and heights.

Specific Objectives

By the end of the lesson, pupils should be able to:

Cognitive Domain:
(a) Identify angles of elevation and depression in diagrams and real-life situations.
(b) Distinguish between angles of elevation and depression.
(c) Calculate heights and distances using angles of elevation and depression.
Affective Domain:
(a) Show interest in applying trigonometric concepts to solve real-life problems.
Psychomotor Domain:
(a) Measure angles using a protractor accurately.
(b) Draw diagrams representing angles of elevation and depression.
Social Domain:
(a) Work collaboratively in pairs or groups to solve problems involving angles of elevation and depression.

Reference Materials

The following resources was used in planning this lesson:

9 Years Basic Education Curriculum
Lagos State Unified Scheme of work for Junior Secondary Schools
Cuemath – Angle of Elevation – Formula | Angle of Depression
Relevant Textbooks

Instructional Materials

The teacher will teach this lesson with the aid of:

Whiteboard and markers
Protractor, ruler, and set squares
Chart showing angles of elevation and depression
Flashcards with problems for practice
Measuring tape for practical demonstration
Scientific calculator

Rationale for the Lesson

This lesson enables pupils to understand and apply angles of elevation and depression in measuring heights and distances, strengthening problem-solving and spatial reasoning skills.

Prerequisite/Previous Knowledge

Pupils should already know basic trigonometric ratios (sine, cosine, tangent), understand right-angled triangles, and be familiar with measuring angles using a protractor.

Lesson Content/Board Summary

Angles Of Elevation And Depression

Angles of elevation and depression are the angles formed when observing an object from a certain point, either looking up or down. They are used to solve real-life problems involving heights and distances.

Identifying Angles of Elevation and Depression

Angles of elevation are formed when an observer looks upward at an object above the horizontal line. Angles of depression are formed when the observer looks downward at an object below the horizontal line.

The following are key points to identify angles:

Draw a horizontal line from the observer’s eye level.
The angle between the horizontal line and the line of sight to the object is the angle of elevation if looking up.
The angle between the horizontal line and the line of sight to the object is the angle of depression if looking down.
Use diagrams to visualize the scenario clearly.

Distinguishing Between Angles of Elevation and Depression

The following are differences:

Angle of elevation – observer looks upward; angle is above the horizontal.
Angle of depression – observer looks downward; angle is below the horizontal.
Both angles are measured from the horizontal line at the observer’s eye level.

Measuring Angles of Elevation and Depression

Angles can be measured using instruments like protractors or calculated using trigonometric ratios.

Examples are:

Using a protractor on a drawn diagram to measure the angle from horizontal.
Applying tan θ = opposite ÷ adjacent to find the angle or distance.
Example: A building 20 m high is observed from a point 30 m away. tan θ = 20 ÷ 30 = 0.6667 → θ ≈ 33.7°

Using Angles of Elevation and Depression in Calculating Distances and Heights

These include practical applications:

Calculating the height of a tree using the angle of elevation and distance from the tree.
Determining the distance of a ship from a cliff using the angle of depression.
Formula: tan θ = height ÷ distance for right-angled triangles.
Example: From a point 50 m from the base of a tower, angle of elevation = 45°. Height of tower = 50 × tan 45° = 50 m.

Teaching Methods/Instructional Techniques:

Discussion, Lecture, Explanation, Demonstration, Question and Answer, Group Work, Visual Aids

Instructional Procedures

To deliver this lesson, the teacher will adopt the following steps:

Step 1: Introduction

Time: 5 minutes
Teaching Skill: Set Induction
Teacher’s Activity: Teacher shows a diagram of a building and a point on the ground, asks pupils how to measure the height without climbing.
Pupils’ Activity: Pupils respond and recall previous lessons on right-angled triangles.
Learning Point: Pupils are introduced to angles of elevation and depression in a real-life context.

Step 2: Identifying Angles of Elevation and Depression

Time: 8 minutes
Teaching Skill: Explanation
Teacher’s Activity: Teacher explains the concepts, draws diagrams on the board, and points out angles of elevation and depression.
Pupils’ Activity: Pupils copy diagrams and identify angles on their exercise books.
Learning Point: Pupils can identify angles in diagrams and real-life situations.

Step 3: Distinguishing Angles of Elevation and Depression

Time: 7 minutes
Teaching Skill: Discussion
Teacher’s Activity: Teacher discusses the differences, highlighting the observer’s perspective and the horizontal line.
Pupils’ Activity: Pupils state the differences and note them down.
Learning Point: Pupils understand the difference between angles of elevation and depression.

Step 4: Measuring Angles

Time: 8 minutes
Teaching Skill: Demonstration
Teacher’s Activity: Teacher demonstrates measuring angles using a protractor and applying tan θ = opposite ÷ adjacent to calculate angles.
Pupils’ Activity: Pupils practice measuring angles on drawn diagrams and perform simple calculations.
Learning Point: Pupils learn to measure angles accurately and apply trigonometry.

Step 5: Using Angles to Calculate Distances and Heights

Time: 10 minutes
Teaching Skill: Problem Solving
Teacher’s Activity: Teacher solves examples on the board using tan θ = height ÷ distance, then assigns similar problems to pupils.
Pupils’ Activity: Pupils solve problems individually or in pairs, showing workings.
Learning Point: Pupils can apply angles of elevation and depression to real-life height and distance problems.

Step 6: Note-Taking

Time: 3 minutes
Teaching Skill: Explanation
Teacher’s Activity: Teacher writes the board summary and explains key points for pupils to copy.
Pupils’ Activity: Pupils take notes carefully.
Learning Point: Pupils have a clear reference for revision.

Step 7: Evaluation/Review

Time: 3 minutes
Teaching Skill: Questioning
Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

Define angles of elevation and depression.
Distinguish between angles of elevation and depression.
Calculate the height of a tree 40 m away with an angle of elevation of 30°.
Measure an angle of depression of 25° on a given diagram.
Pupils’ Activity: Pupils answer orally and solve problems on paper.
Learning Point: Pupils demonstrate understanding and mastery of the lesson objectives.

Step 8: Conclusion

Time: 1 minute
Teaching Skill: Reinforcement
Teacher’s Activity: Teacher summarizes the lesson, reinforces formulas, and encourages pupils to practice.
Pupils’ Activity: Pupils listen and ask clarifying questions.
Learning Point: Pupils consolidate understanding of angles of elevation and depression.

Lesson Keywords

Angle of Elevation – angle formed looking upward from horizontal
Angle of Depression – angle formed looking downward from horizontal
Right-Angled Triangle – triangle with one angle equal to 90°
Opposite Side – side opposite the angle of interest in a triangle
Adjacent Side – side next to the angle of interest in a triangle

Differentiation

Provide simpler diagrams and guided examples for slower learners, while advanced pupils solve complex problems involving multiple triangles or real-life scenarios.

Note for teachers using this lesson plan

Use real-life demonstrations when possible, such as measuring objects in the classroom or school environment. Encourage accurate diagram drawing and emphasize proper formula application.