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Exploring Right Triangle Properties: Finding Side Lengths Using Special Ratios

In this lesson, we delve into the patterns found in right triangles, focusing on how to calculate the lengths of sides using given angles and one side length. Specifically, we will analyze the properties of special right triangles, including the 30-60-90 and 45-45-90 triangle types. By utilizing reference triangles and proportions, students will learn how to find missing side lengths through practical examples. This understanding will enhance their problem-solving skills and grasp of geometric relationships.

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Exploring Right Triangle Properties: Finding Side Lengths Using Special Ratios

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  1. Math II UNIT QUESTION: What patterns can I find in right triangles? Standard: MM2G1, MM2G2 Today’s Question: How do I find the length of a side of a right triangle with only one side and an angle given? Standard: MM2G1.a

  2. 5.1 Special Right Triangles Learning Task – Part 1

  3. 5.1 Special Right Triangles You will be able to find the lengths of sides of special right triangles 30-60-90 And 45-45-90

  4. 30-60-90

  5. Special Right Triangles Short Leg:Long Leg:Hypotenuse

  6. We will use a reference triangle to set up a proportion then solve. 30-60-90 Right Triangle 60 2 1 30 This is our reference triangle for the 30-60-90 triangle.

  7. 30-60-90 Right Triangle 60 2x x 30

  8. Ex: 1 Solve for x and y. 60 8 2a x a 30 y a√3

  9. Solve for x and y Ex: 2 y a√3 30 x a 2a 24 60

  10. Ex: 3 Solve for x and y. 30 2a 14 y a√3 60 x a y = 7√3 x = 7

  11. Ex: 4 Solve for x and y a x a√3 60 30 y 2a y = 10 x = 5

  12. Extension Problem The altitude of an equilateral triangle is 8 inches. Find the perimeter of the triangle. 30° 2a a√3 8 60° a a = 4.168 in., so 2a = 9.238 in. Perimeter = 27.71 inches

  13. Homework Page 155 #1-7 (odd), 14, 17-21

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