Lesson Notes By Weeks and Term v5 - Grade 9

Lesson Video

This page supports the lesson note with a companion video and a short classroom-ready summary.

For class groups and homework, share this lesson page so learners also get the summary, objectives, and full lesson context.

Performance objectives

• Apply the Pythagorean Theorem to find sides of right-angled triangles.
• Identify the hypotenuse, opposite, and adjacent sides.
• Calculate sine, cosine, and tangent ratios.
• Use trig ratios to find unknown sides.
• Solve real-world problems.

Lesson summary

This week, we delve into the fascinating world of measurement and trigonometry, focusing specifically on applying the Pythagorean Theorem and understanding the basics of trigonometric ratios (sine, cosine, and tangent) in right-angled triangles. Measurement is fundamental to our daily lives, from cooking and construction to navigation and sports. Trigonometry, meaning "triangle measurement," extends this by allowing us to calculate unknown lengths and angles in triangles, especially right-angled triangles. This is incredibly useful in surveying, engineering, architecture, and even astronomy.

Lesson notes

2.1 The Pythagorean Theorem The Pythagorean Theorem is a fundamental concept in geometry that relates the sides of a right-angled triangle. A right-angled triangle has one angle that is exactly 90 degrees. The side opposite the right angle is called the hypotenuse (and is the longest side). The other two sides are called legs.

Theorem: In a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).

Formula: a² + b² = c² Why does it work? Visually, imagine squares drawn on each side of the right-angled triangle. The area of the square on the hypotenuse is equal to the combined area of the squares on the other two sides.