Math Example--Right Triangles-- Example 7

Topic

Right Triangles

Description

This example presents a right triangle with sides x and y in a 5:12 ratio, and an unknown hypotenuse c. The goal is to express c in terms of the ratio. Using the Pythagorean Theorem, we find that x = 5p, y = 12p, and c = √((5p)² + (12p)²) = 13p. This demonstrates how the 5-12-13 Pythagorean triple can be generalized.

This example builds upon previous ones by combining the concepts of ratios and Pythagorean triples. It helps students understand how to work with variable expressions in right triangles and recognize the underlying patterns in Pythagorean triples.

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 explore different aspects of right triangles, helping students develop problem-solving skills and a deeper understanding of geometric relationships.

Teacher's Script: Let's look at our seventh example. This time, we have a right triangle where the sides are in a 5:12 ratio. How is this similar to or different from what we've seen before? Our task is to express the hypotenuse c in terms of these ratios. How can we apply the Pythagorean Theorem here? Let's work through this together and see if we can spot any connections to our previous examples.

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