Math Example--Right Triangles-- Example 18

Topic

Right Triangles

Description

This example features a right triangle with one leg measuring 5 units, an unknown leg b, and a hypotenuse of 13 units. Using the Pythagorean Theorem, we calculate that b = √(13² - 5²) = √(169 - 25) = √(144) = 12. This demonstrates that the triangle is a special Pythagorean Triple with sides in the ratio 5:12:13.

This example introduces a new Pythagorean triple, 5-12-13, which is less common than the 3-4-5 triple but equally important. Understanding various Pythagorean triples helps students recognize patterns in right triangles and develop problem-solving strategies for more complex geometric scenarios.

Exposing students to multiple worked examples is essential for developing a comprehensive understanding of right triangles and their properties. Each new example provides an opportunity to explore different types of right triangles, helping students recognize patterns and build problem-solving skills that can be applied to various geometric scenarios.

Teacher's Script: Now, let's look at our eighteenth example. We have a right triangle where we know one leg and the hypotenuse. What do you notice about these numbers? They're different from what we've seen before, aren't they? Let's solve for b and see what we discover. As we work through this, think about how this triangle might be similar to or different from the 3-4-5 triangles we've studied.

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