S3 Mathematics - Term 1

Topic 1: Trigonometry I

Lesson 1: Introduction to Trigonometry

Duration: 40 minutes

Learning Outcomes

By the end of this lesson, you should be able to:

• Understand what trigonometry is and its applications
• Identify the parts of a right-angled triangle
• Recognize the relationship between angles and sides

Real-World Questions

• How do surveyors measure the height of a mountain?
• How do architects calculate roof slopes?
• How do pilots navigate using angles?

Trigonometry helps answer all these questions!

What is Trigonometry?

From Greek:

• "trigonon" = triangle
• "metron" = measure

Trigonometry = Triangle Measurement

The study of relationships between angles and sides in triangles

Parts of a Right-Angled Triangle

The Three Parts

For any right-angled triangle, relative to an angle:

1. Hypotenuse - Longest side, opposite the 90 degrees angle
2. Opposite - Side across from our angle
3. Adjacent - Side next to our angle (not hypotenuse)

Important!

The labels change depending on which angle you're looking at!

Hypotenuse - always the same
Opposite and Adjacent - depend on your reference angle

Pair Practice

1. Draw a right-angled triangle in your notebook
2. Label the hypotenuse
3. Choose one acute angle and mark it
4. Label the opposite and adjacent sides

Partner checks your work!

Similar Triangles Discovery

The Big Discovery

For any specific angle:

The ratio of sides is CONSTANT

• Triangle size doesn't matter
• Only the angle matters
• This is the foundation of trigonometry!

Example

Two triangles, both with a 30 degrees angle:

Small triangle: opposite/hypotenuse = 3/6 = 0.5
Large triangle: opposite/hypotenuse = 6/12 = 0.5

Same angle = Same ratio!

Group Activity

In your groups:

1. Draw a right-angled triangle with a 60 degrees angle
2. Measure the opposite and hypotenuse carefully
3. Calculate: opposite divided by hypotenuse
4. Compare your ratio with other groups

What do you notice?

Summary

• Trigonometry = triangle measurement
• Right-angled triangles have three labeled parts
• Labels depend on the reference angle
• Same angle = same ratio (regardless of triangle size)

Why This Matters

This constant ratio property means:

• We can measure ONE angle and ONE side
• And find ALL other parts!
• This makes trigonometry incredibly useful

Coming Up

Next lessons:

• The unit circle
• Sine, cosine, and tangent
• Solving real problems with trigonometry

Exit Question

Draw a right-angled triangle and:

1. Label the hypotenuse
2. Mark one acute angle as theta (θ)
3. Label the opposite and adjacent sides

Homework

1. Draw three different right-angled triangles
2. For each: mark right angle, choose angle theta, label all parts
3. For one triangle: measure opposite and hypotenuse, calculate the ratio

Time: 15-20 minutes

Credits

Created: December 2025
Based on: NCDC Lower Secondary Mathematics Syllabus (2019)

Source: National Curriculum Development Centre (NCDC), Uganda