Class: Junior Secondary School 3 (JSS3, JSS 3)
Term: 2nd Term
Week: 7
Age: 14 years
Duration: 45 minutes
Subject: Mathematics
Curriculum Theme: Mathematics
Previous Lesson: Enlargement and Scale Factor
Topic: Trigonometry
Subject Matter: Identify sine, cosine and tangent of an acute angle as ratios of sides of a right-angled triangle, Using trigonometric ratio to solve practical problems, Applying trigonometric ratios to solve word problems.

Specific Objectives

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

Cognitive Domain:
(a) Explain the meaning of sine, cosine and tangent as ratios of sides of a right-angled triangle.
(b) Use trigonometric ratios to solve numerical and word problems.
Affective Domain:
(a) Appreciate the relevance of trigonometry in real-life situations such as heights and distances.
Psychomotor Domain:
(a) Demonstrate the ability to identify and label sides of right-angled triangles for trigonometric calculations.
Social Domain:
(a) Work cooperatively in groups to solve trigonometric problems.

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
Britannica – Trigonometry | Definition, Formulas, Ratios, & Identities
Relevant Textbooks

Instructional Materials

The teacher will teach this lesson with the aid of:

Chart showing right-angled triangles
Scientific calculators
Rulers and protractors
Graph sheets
Whiteboard and markers

Rationale for the Lesson

Trigonometry helps learners understand the relationships between angles and sides of right-angled triangles and equips them with skills to solve real-life practical problems.

Prerequisite/Previous Knowledge

Pupils already know the basic properties of triangles, types of angles and how to identify right-angled triangles.

Lesson Content/Board Summary

Lesson Content

Trigonometry

Meaning of Trigonometric Ratios

Trigonometric ratios describe the relationships between the angles and sides of a right-angled triangle. These ratios help to calculate unknown sides or angles.
The following are the trigonometric ratios in a right-angled triangle:

Sine (sin θ) = Opposite / Hypotenuse
Cosine (cos θ) = Adjacent / Hypotenuse
Tangent (tan θ) = Opposite / Adjacent

Identifying Sides of a Right-Angled Triangle

A right-angled triangle has one angle measuring 90°. The longest side is the hypotenuse while the other two sides are named based on their position relative to the angle being considered.
These include:

Opposite side – the side facing the angle.
Adjacent side – the side next to the angle but not the hypotenuse.
Hypotenuse – the longest side opposite the right angle.

Using Trigonometric Ratios to Solve Problems

Trigonometric ratios help in calculating unknown lengths and angles when one side and one angle (other than the right angle) are known.
Examples include:

To find a missing side using sine, cosine or tangent.
To determine an unknown acute angle using inverse trigonometric functions.

Word Problems Involving Trigonometric Ratios

Trigonometry is applied in real-life problems such as calculating the height of a tree, building or pole using angles of elevation or depression.
Examples are:

Finding the height of an object when its distance from an observer and angle of elevation are known.
Determining the distance between two points using angles and side lengths.

Teaching Methods/Instructional Techniques:

Discussion, Lecture, Explanation, Demonstration, 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: The teacher reviews the previous lesson and shows a chart of a right-angled triangle, asking pupils to identify its sides.
Pupils’ Activity: Pupils observe the chart and respond to the teacher’s questions.
Learning Point: Pupils recall triangle properties and right-angle identification.

Step 2: Meaning of Trigonometric Ratios

Time: 10 minutes
Teaching Skill: Explanation
Teacher’s Activity: The teacher defines sine, cosine and tangent and explains the SOH-CAH-TOA relationship.
Pupils’ Activity: Pupils listen and identify the ratios on the chart.
Learning Point: Pupils understand trigonometric ratios as side relationships.

Step 3: Identifying Sides

Time: 10 minutes
Teaching Skill: Demonstration
Teacher’s Activity: The teacher labels sides of a sample triangle and shows how to identify opposite, adjacent and hypotenuse based on the given angle.
Pupils’ Activity: Pupils practise labeling sides on their worksheets.
Learning Point: Pupils can correctly identify triangle sides for trigonometric use.

Step 4: Solving Trigonometric Problems

Time: 10 minutes
Teaching Skill: Guided Practice
Teacher’s Activity: The teacher solves examples on finding missing sides and angles using trigonometric ratios.
Pupils’ Activity: Pupils attempt similar classwork problems.
Learning Point: Pupils apply trigonometric ratios in solving problems.

Step 5: Note-Taking

Time: 3 minutes
Teaching Skill: Reinforcement
Teacher’s Activity: The teacher guides pupils to write the board summary.
Pupils’ Activity: Pupils copy the note into their notebooks.
Learning Point: Pupils retain key points of the lesson.

Step 6: Evaluation/Review

Time: 5 minutes
Teaching Skill: Assessment
Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

What is sine of an angle?
Identify the hypotenuse in a right-angled triangle.
Solve: If tan θ = 3/4, find opposite side when adjacent is 12 cm.
Mention two applications of trigonometric ratios.
Pupils’ Activity: Pupils answer the questions.
Learning Point: Pupils demonstrate understanding of the lesson objectives.

Step 7: Conclusion

Time: 2 minutes
Teaching Skill: Closure
Teacher’s Activity: The teacher summarizes the lesson and highlights the importance of trigonometry in real life.
Pupils’ Activity: Pupils listen and ask questions if necessary.
Learning Point: Pupils consolidate knowledge gained.

Lesson Keywords

Trigonometry – study of relationships between triangle sides and angles
Hypotenuse – longest side of a right-angled triangle
Sine – ratio of opposite side to hypotenuse
Cosine – ratio of adjacent side to hypotenuse
Tangent – ratio of opposite side to adjacent

Differentiation

Provide additional simplified diagrams for slower learners while advanced learners solve extra application problems; pair weaker pupils with stronger peers.

Note for teachers using this lesson plan

Ensure pupils understand side identification before introducing trigonometric ratios. Use real-life examples like trees, poles and buildings to aid comprehension.