Math Example--Right Triangles-- Example 11

Topic

Right Triangles

Description

This example introduces a 30-60-90 right triangle with the shorter leg measuring 1 unit, the longer leg sqrt(3), and an unknown hypotenuse c. Using the Pythagorean Theorem, we calculate that c = √(1² + (√(3))²) = √(1 + 3) = 2. This demonstrates that the side lengths are in the ratio 1 : √(3) : 2, a fundamental relationship in 30-60-90 triangles.

30-60-90 triangles are important in geometry due to their unique angle measures and side length ratios. Understanding these special right triangles helps students solve problems involving equilateral triangles and hexagons, as well as many real-world applications.

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 types 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 eleventh example. We have a different type of right triangle here. Can anyone identify what's special about its angles? That's right, it's a 30-60-90 triangle. Notice how the side lengths are different from what we've seen before. Let's work through this example and discover the unique ratio that these triangles always follow. How do you think this ratio might be useful in solving other geometric problems?

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