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11.5 Two Special Right Triangles

11.5 Two Special Right Triangles. 45°- 45°- 90° 30°- 60°- 90°. 45°-45°-90° Special Right Triangle. In a triangle 45°-45°-90° , the hypotenuse is times as long as a leg. Example:. 45°. 45°. 5 cm. Hypotenuse. 5 cm. Leg. X. X. 45°. 5 cm. 45°. Leg. X. 45°. 2. 1.

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11.5 Two Special Right Triangles

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  1. 11.5 Two Special Right Triangles 45°- 45°- 90° 30°- 60°- 90°

  2. 45°-45°-90° Special Right Triangle • In a triangle 45°-45°-90° , the hypotenuse is times as long as a leg. Example: 45° 45° 5 cm Hypotenuse 5 cm Leg X X 45° 5 cm 45° Leg X Lesson 7-3: Special Right Triangles

  3. 45° 2 1 45° 1 45°- 45°- 90° Conclusion: the ratio of the sides in a 45-45-90 triangle is 1-1-2

  4. 45° 4 45° 45°- 45°- 90° Practice 4 2 4 SAME leg*2

  5. 45° 9 45° 45°- 45°- 90° Practice 9 2 9 SAME leg*2

  6. 45° 2 45° 45°- 45°- 90° Practice 2 2 2 SAME leg*2

  7. 45° 7 45° 45°- 45°- 90° Practice 14 7 SAME leg*2

  8. 45°- 45°- 90° Practice Now Let's Go Backward

  9. 45° 45° 45°- 45°- 90° Practice 3 2 hypotenuse2

  10. 3 2 2 45°- 45°- 90° Practice = 3

  11. 45° 45° 45°- 45°- 90° Practice 3 2 3 3 SAME hypotenuse2

  12. 45° 45° 45°- 45°- 90° Practice 6 2 hypotenuse2

  13. 6 2 2 45°- 45°- 90° Practice = 6

  14. 45° 45° 45°- 45°- 90° Practice 6 2 6 6 SAME hypotenuse2

  15. 45° 45° 45°- 45°- 90° Practice 11 2 hypotenuse2

  16. 11 2 2 45°- 45°- 90° Practice = 11

  17. 45° 45° 45°- 45°- 90° Practice 112 11 11 SAME hypotenuse2

  18. 45° 45° 45°- 45°- 90° Practice 8 hypotenuse2

  19. 8 2 82 = * 2 2 2 45°- 45°- 90° Practice = 42

  20. 45° 45° 45°- 45°- 90° Practice 8 42 42 SAME hypotenuse2

  21. 45° 45° 45°- 45°- 90° Practice 4 hypotenuse2

  22. 4 2 42 = * 2 2 2 45°- 45°- 90° Practice = 22

  23. 45° 45° 45°- 45°- 90° Practice 4 22 22 SAME hypotenuse2

  24. 45° 45° 45°- 45°- 90° Practice 6 Hypotenuse 2

  25. 6 2 62 = * 2 2 2 45°- 45°- 90° Practice = 32

  26. 45° 45° 45°- 45°- 90° Practice 6 32 32 SAME hypotenuse2

  27. 30° 60° 30°- 60°- 90° This creates the 30-60-90 triangle with a hypotenuse a short leg and a long leg. Long Leg hypotenuse Short Leg

  28. X 5 cm 30°-60°-90° Special Right Triangle • In a triangle 30°-60°-90° , the hypotenuse is twice as long as the shorter leg, and the longer leg is times as long as the shorter leg. Example: Hypotenuse 30° 2X Longer Leg 30° 10 cm 60° 60° X Shorter Leg 5 cm Lesson 7-3: Special Right Triangles

  29. 30° 60° 30°- 60°- 90° Conclusion: the ratio of the sides in a 30-60-90 triangle is 1- 2 - 3 2 3 1

  30. 30° 60° 30°- 60°- 90° Practice The key is to find the length of the short side. 8 43 Hypotenuse = short leg * 2 4 Long Leg = short leg *3

  31. 30° 60° 30°- 60°- 90° Practice 10 Hypotenuse = short leg * 2 53 5 Long Leg = short leg *3

  32. 30° 60° 30°- 60°- 90° Practice 14 Hypotenuse = short leg * 2 73 7 Long Leg = short leg *3

  33. 30° 60° 30°- 60°- 90° Practice 23 Hypotenuse = short leg * 2 3 3 Long Leg = short leg *3

  34. 30° 60° 30°- 60°- 90° Practice 210 30 Hypotenuse = short leg * 2 10 Long Leg = short leg *3

  35. 30°- 60°- 90° Practice Now Let's Go Backward

  36. 30° 60° 30°- 60°- 90° Practice 22 Short Leg = Hypotenuse 2 113 11 Long Leg = short leg *3

  37. 30° 60° 30°- 60°- 90° Practice 4 Short Leg = Hypotenuse 2 23 2 Long Leg = short leg *3

  38. 30° 60° 30°- 60°- 90° Practice 18 Short Leg = Hypotenuse 2 93 9 Long Leg = short leg *3

  39. 30° 60° 30°- 60°- 90° Practice 30 Short Leg = Hypotenuse 2 153 15 Long Leg = short leg *3

  40. 30° 60° 30°- 60°- 90° Practice 46 Hypotenuse = Short Leg * 2 233 23 Short Leg = Long leg 3

  41. 30° 60° 30°- 60°- 90° Practice 28 Hypotenuse = Short Leg * 2 143 14 Short Leg = Long leg 3

  42. 30° 60° 30°- 60°- 90° Practice 32 Hypotenuse = Short Leg * 2 163 16 Short Leg = Long leg 3

  43. 30° 60° 30°- 60°- 90° Practice 63 Hypotenuse = Short Leg * 2 9 3 3 Short Leg = Long leg 3

  44. 30° 60° 30°- 60°- 90° Practice 83 Hypotenuse = Short Leg * 2 12 4 3 Short Leg = Long leg 3

  45. 30° 60° 30°- 60°- 90° Practice 183 Hypotenuse = Short Leg * 2 27 9 3 Short Leg = Long leg 3

  46. 30° 60° 30°- 60°- 90° Practice 143 Hypotenuse = Short Leg * 2 21 7 3 Short Leg = Long leg 3

  47. 30° 60° 30°- 60°- 90° Practice 223 Hypotenuse = Short Leg * 2 33 113 Short Leg = Long leg 3

  48. Homework • Page 585 (1-6, 8-15) all

  49. THE END

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