Learn: Pythagoras' Theorem in 2D Contexts

Welcome!Today we'll explore Pythagoras' Theorem, a key concept for working with right-angled triangles. It's useful for solving problems involving distances or lengths. Let's get started!

What is Pythagoras' Theorem?Pythagoras' Theorem states that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. This can be written as a² + b² = c², where c is the hypotenuse.

Why is Pythagoras' Theorem important?This theorem helps us calculate unknown lengths in right-angled triangles, which is useful for solving real-world problems like measuring distances, calculating heights, or designing structures.

How to Use Pythagoras' TheoremTo find a missing side, rearrange the formula a² + b² = c². For example, if you need the hypotenuse, calculate c = √(a² + b²). If you need a shorter side, use a² = c² - b².

Example: Finding the HypotenuseImagine a right-angled triangle with sides 3 cm and 4 cm. To find the hypotenuse, calculate:c² = 3² + 4²c² = 9 + 16c² = 25c = √25 = 5 cm

Finding a Shorter SideIf the hypotenuse and one side are known, you can find the missing side. For example, if the hypotenuse is 10 cm and one side is 6 cm, calculate:a² = c² - b²a² = 10² - 6²a² = 100 - 36a² = 64a = √64 = 8 cm

Real-World ApplicationsPythagoras' Theorem is used in construction (e.g., to ensure structures are level), navigation (e.g., finding distances between points), and even in sports for calculating trajectories or angles.

Review Time!Great work! You've learned about Pythagoras' Theorem, how to use it, and some real-world applications. Let's test your understanding with a few final questions.