Math Example--Right Triangles-- Example 16

Topic

Right Triangles

Description

This example features a right triangle with one leg measuring 6 units, an unknown leg b, and a hypotenuse of 10 units. Applying the Pythagorean Theorem, we calculate that b = √(c² - a²) = √(10² - 6²) = √(64) = 8. This demonstrates that the side lengths are in the ratio 3:4:5, a scaled version of the Pythagorean triple we saw in the previous example.

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.

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 look at our sixteenth 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 3-4-5 triangle we just saw?

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