Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 13

Topic

Ratios, Proportions, and Percents

Description

This example demonstrates solving a proportion problem using similar right triangles with special angles (30°-60°-90°). Two triangles are shown, with the smaller one having sides of 6√3 and 6, and the larger one having sides of x and 12. The problem requires finding the length of side x by setting up a proportion: (6√3) / 6 = x / 12. Solving this equation leads to x = 12√3.

Understanding proportions in geometric contexts, particularly with special right triangles, is a crucial skill in mathematics. This collection of examples helps teach the topic by presenting various scenarios where proportions are applied to solve problems involving trigonometric ratios, allowing students to see the connection between geometry, algebra, and trigonometry.

Exposure to multiple worked-out examples is essential for students to fully grasp proportions and their applications in advanced geometric scenarios. Each example reinforces the core concept while introducing different aspects of special triangles, helping students develop problem-solving skills and recognize patterns across various types of proportion problems involving irrational numbers and trigonometric relationships.

Teacher's Script: "In this example, we're using similar 30°-60°-90° triangles to set up a proportion. Notice how we're working with the square root of 3. Let's solve this step-by-step, showing you how to apply proportion concepts to problems involving special right triangles. This skill will be valuable in trigonometry and calculus, as well as in fields like physics and engineering."

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