Math Example--Right Triangles-- Example 12

Topic

Right Triangles

Description

This example presents a 30-60-90 right triangle with the shorter leg measuring 4 units, the longer leg 4 * sqrt(3), and an unknown hypotenuse c. Applying the Pythagorean Theorem, we calculate that c = √((4)² + (4 * √(3))²) = √(16 + 16 * 3) = √(64) = 8. This demonstrates that the side lengths are in the ratio 1 : √(3) : 2, scaled by a factor of 4.

This example builds upon the previous one, showing how the 1 : √(3) : 2 ratio applies even when the leg length changes. It helps students understand the scalability of these relationships in 30-60-90 triangles and reinforces the concept of proportionality in geometry.

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 reinforce concepts, recognize patterns, and build problem-solving skills that can be applied to more complex geometric scenarios.

Teacher's Script: Let's examine our twelfth example. We have another 30-60-90 triangle, but this time with different side lengths. What do you notice about these lengths compared to our previous example? That's right, they're all 4 times larger. Let's work through this problem and see how it relates to what we learned before. Can you predict what the hypotenuse will be based on the pattern we've observed?

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