Math Example--Right Triangles-- Example 24

Topic

Right Triangles

Description

This example features a 30-60-90 right triangle with a hypotenuse of 2, a shorter leg (adjacent to the 30° angle) of 1, and an unknown longer leg b (adjacent to the 60° angle). Applying the Pythagorean Theorem, we calculate that b = √(2² - 12) = √(4 - 1) = √(3). This demonstrates the special properties of 30-60-90 triangles, where the sides are in the ratio 1 : √(3) : 2.

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 twenty-fourth 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 the 45-45-90 triangles we've been working with. Let's solve for b and see if we can 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.