Math Example--Right Triangles-- Example 4

Topic

Right Triangles

Description

This example introduces a right triangle with sides in a 3:4 ratio, labeled x and y, and an unknown hypotenuse c. The goal is to express c in terms of the ratio. Using the Pythagorean Theorem, we find that x = 3p, y = 4p, and c = √((3p)² + (4p)²) = √(25p²) = 5p.

This example builds upon previous ones by introducing the concept of ratios in right triangles. It demonstrates how the Pythagorean Theorem can be applied to triangles with sides expressed in terms of a variable, helping students understand more complex applications of the theorem.

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

Teacher's Script: Let's examine our fourth example. This time, we have a right triangle where the sides are in a 3:4 ratio. What do you notice about how the sides are labeled? That's right, we're using variables. Our task is to express the hypotenuse c in terms of these ratios. How do you think we can approach this using the Pythagorean Theorem? Let's work through this together and see how we can apply what we've learned to this new situation.

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