Math Example--Right Triangles-- Example 13

Topic

Right Triangles

Description

This example features a 30-60-90 right triangle with sides labeled x and y, and hypotenuse c. The side lengths are in the ratio 1 : √(3) : 2. Given that x = 1 * p and y = √(3) * p, we solve for c using the Pythagorean Theorem: c = √(p² + (√(3) * p)²) = √(4p²) = 2p. This demonstrates how the 1 : √(3) : 2 ratio applies generally to all 30-60-90 triangles.

This example generalizes the concept of 30-60-90 triangles, showing that the 1 : √(3) : 2 ratio holds true for any scale factor p. It helps students understand the algebraic representation of geometric relationships and how variables can be used to express general rules in mathematics.

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 explore different aspects of right triangles, helping students recognize patterns and build problem-solving skills that can be applied to various geometric scenarios.

Teacher's Script: Now, let's look at our thirteenth example. We have another 30-60-90 triangle, but this time the sides are labeled with variables. What does this mean? That's right, we're looking at a general case. Our task is to express the hypotenuse c in terms of p. As we work through this, think about how this relates to our previous examples. How does using variables help us understand the general properties of 30-60-90 triangles?

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