Math Example--Right Triangles-- Example 19

Topic

Right Triangles

Description

This example presents a right triangle with one leg measuring 10 units, an unknown leg b, and a hypotenuse of 26 units. Applying the Pythagorean Theorem, we calculate that b = √(26² - 10²) = √(676 - 100) = √(576) = 24. This demonstrates that the triangle is a scaled version of the 5-12-13 Pythagorean Triple, with all sides doubled.

This example builds upon the previous one, showing 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.

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

Teacher's Script: Let's examine our nineteenth example. We have another right triangle where we know one leg and the hypotenuse. What do you notice about these numbers compared to our previous example? That's right, they're larger but still whole numbers. Let's solve for b and see if we can spot a pattern. How do you think this triangle might be related to the 5-12-13 triangle we just saw?

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