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Special Right Triangles

Special Right Triangles. 30:60:90 Right Triangles. 30:60:90 Relationship. Given: Equilateral Triangle with side=2, find the altitude. 30 º. 2. 2. x. 60 º. 1. 2. 30:60:90 Relationship. Given: Equilateral Triangle with side=4, find the altitude. 30 º. 4. 4. x. 60 º. 2. 4.

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Special Right Triangles

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  1. Special Right Triangles 30:60:90 Right Triangles

  2. 30:60:90 Relationship • Given: Equilateral Triangle with side=2, find the altitude. 30º 2 2 x 60º 1 2

  3. 30:60:90 Relationship • Given: Equilateral Triangle with side=4, find the altitude. 30º 4 4 x 60º 2 4

  4. 30:60:90 Relationship • Given: Equilateral Triangle with side=10, find the altitude. 30º 10 10 x 60º 5 10

  5. Conclusion - The side opposite the 30º angle is half the hypotenuse 30º - The side opposite the 60º angle is half the hypotenuse times 2 1 - The ratio of the sides of a 30:60:90 right triangle is 60º 1

  6. Page 25 Remember, the 30-60-90 triangle always has the same ratio for its sides: Remember the relationship the sides have with the angles! The smallest side is across from the smallest angle! Since 30 is the smallest angle, then the 1 goes across from it! Since 60 is the next biggest angle, then the goes across from it! Since 90 is the largest angle, then the 2 goes across from it!

  7. Page 26 Now, since the ratio is always the same, then what did we multiply by? Five! If we multiply one number in the ratio by 5, we multiply all of them by 5.

  8. Page 26 Multiply by 10

  9. Page 26 Multiply by 1

  10. Page 26 Multiply by 15

  11. Page 26 If you see this on the Regents and is a multiple choice question, compare decimals to the answer given.

  12. Page 26 Multiply by 5

  13. Page 26 Multiply by 8 6

  14. Page 26 Multiply by 2

  15. Page 26 Multiply by 3.5

  16. Page 26 Multiply by 7.5

  17. Page 26 Multiply by

  18. Page 26 Multiply by 7

  19. Page 26 Multiply by 5

  20. Page 26 Multiply by 4

  21. Page 26 Multiply by 5

  22. Page 26 Multiply by 4 :

  23. Homework • Page 26 #12,14,16,19 Separate Sheet

  24. Page 26 C Multiply by 4 B A

  25. Page 26 Multiply by 5 Multiply by

  26. Page 26 Multiply by 3 Multiply by 6

  27. Page 26 Multiply by 6 Multiply by 12

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