Math Example--Right Triangles-- Example 15

Topic

Right Triangles

Description

This example presents a right triangle with one leg measuring 3 units, an unknown leg b, and a hypotenuse of 5 units. Using the Pythagorean Theorem, we calculate that b = √(c² - a²) = √(5² - 3²) = √(16) = 4. This triangle demonstrates the 3-4-5 Pythagorean triple, a fundamental relationship in right triangles.

Pythagorean triples are sets of three positive integers that satisfy the Pythagorean Theorem. The 3-4-5 triple is the smallest and most well-known of these. Understanding these special cases helps students recognize patterns and develop a deeper appreciation for the properties of right triangles.

Providing multiple worked examples is crucial for students to fully grasp the concept of right triangles and their various applications. Each new example offers an opportunity to reinforce previously learned concepts while introducing new ideas, helping students build a comprehensive understanding of right triangle geometry.

Teacher's Script: Let's examine our fifteenth example. We have a right triangle where we know one leg and the hypotenuse, and we need to find the other leg. What do you notice about the numbers in this triangle? That's right, they're all whole numbers. As we solve for b, I want you to think about why this particular set of numbers might be special. Can you predict what b will be before we calculate it?

For a complete collection of math examples related to Right Triangles click on this link: Math Examples: Right Triangles Collection.