Math Example--Right Triangles-- Example 6

Topic

Right Triangles

Description

This example features a right triangle with sides measuring 10 and 24 units, and an unknown hypotenuse c. The task is to determine the value of c using the Pythagorean Theorem. By applying the formula a² + b² = c², we calculate that c = √(10² + 24²) = √(676) = 26. This triangle is noted as a scaled version of the 5-12-13 Pythagorean triple.

This example builds upon the previous one, demonstrating how Pythagorean triples can be scaled to create new right triangles with integer side lengths. It helps students understand the relationship between different right triangles and how patterns can emerge in their side lengths.

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 reinforce concepts, recognize patterns, and build problem-solving skills that can be applied to more complex geometric scenarios.

Teacher's Script: Now, let's examine our sixth example. We have a right triangle with sides 10 and 24. What do we need to find? Correct, we're looking for the length of the hypotenuse, c. Let's use the Pythagorean Theorem to solve this. As we work through it, I want you to think about how this triangle might be related to the one we just saw in the previous example. Can you spot any connections?

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