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5.1 Special Right Triangles

5.1 Special Right Triangles. *You will be able to find the lengths of sides of special right triangles. 45-45-90 And 30-60-90. Special Right Triangles. Leg:Leg:Hypotenuse. Short Leg:Long Leg:Hypotenuse. We will use a reference triangle to set up a proportion then solve.

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5.1 Special Right Triangles

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  1. 5.1 Special Right Triangles *You will be able to find the lengths of sides of special right triangles 45-45-90 And 30-60-90

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

  3. We will use a reference triangle to set up a proportion then solve. In a 45-45-90 triangle… LEGS ARE THE SAME LENGTH

  4. 45-45-90 Right Triangle 1 1 This is our reference triangle for the 45-45-90.

  5. 45-45-90 Right Triangle x x

  6. EX: 1 Solve for x Let’s set up a proportion by using our reference triangle. x 3 1 3 x 3 1 1

  7. EX: 2 Solve for x x 5 1 5 x 5 1 1

  8. EX: 3 Solve for x x 3 45 3 1 1 1 x

  9. 30-60-90

  10. 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.

  11. 30-60-90 Right Triangle 60 2x x 30

  12. Ex: 1 60 8 60 2 x 1 30 30 y y 8 x 8 2 1 2

  13. Solve for x Ex: 2 30 60 2 x 1 24 60 30 x 24 2 1 2x = 24 x = 12

  14. Ex: 3 30 60 2 14 1 y 30 60 x y 14 x 2 14 2 1 2x = 14 x = 7

  15. Ex: 4 x 60 2 1 60 30 y 30 x y 1 2 y = 10 x = 5

  16. Classwork

  17. Homework Book Page

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