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SPECIAL RIGHT TRIANGLES:

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hiroko-boyer
29 diapositives · 651 Views · Nov 13, 2014

SPECIAL RIGHT TRIANGLES:. But first, a short video introduction on TRIANGLES:. REMEMBER THESE FACTS:. Angles are on the INSIDE of a Triangle. Sides are the LINES of a Triangle. Angles are written in degrees (90 ◦, 30◦, 45◦). All the angles in ANY Triangle always add up to 180 ◦.

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  1. SPECIAL RIGHT TRIANGLES:

  2. But first, a short video introduction on TRIANGLES:

  3. REMEMBER THESE FACTS: Angles are on the INSIDE of a Triangle. Sides are the LINES of a Triangle. Angles are written in degrees (90◦, 30◦, 45◦) All the angles in ANY Triangle always add up to 180◦

  4. RIGHT TRIANGLE & SPECIAL RIGHT TRIANGLES: 45º 45º 60º 30º

  5. WHY SPECIAL RIGHT TRIANGLES: We use these 2 Special Right Triangles when we need to find the LENGTH of an unknown side of a RIGHT TRIANGLE. We use The PYTHAGOREAN THEOREM formula when you know TWO side lengths of a RIGHT TRIANGLE. We use the SPECIAL RIGHT TRIANGLE formulas when we know ONE side of either type of SPECIAL RIGHT TRIANGLE.

  6. Pythagorean Theorem: We use it when we know the length of 2 SIDES of a Right Triangle and we need to find the length of the unknown side. a² + b² = c² c a b

  7. Example of when to use the Pythagorean Theorem: What is the length of the missing side? ? 10 in 14 in a² + b² = c²

  8. Example of when to use the Pythagorean Theorem: What is the length of the missing side? ? 12 in 18 in a² + b² = c²

  9. Example of when to use the Pythagorean Theorem: What is the length of the missing side? ? 25 in 36 in a² + b² = c²

  10. Example of when to use the Pythagorean Theorem: What is the length of the missing side? ? 14.5 in 18.5 in a² + b² = c²

  11. Example of when to use the Pythagorean Theorem: What is the length of the missing side? 25 in 10 in ? a² + b² = c²

  12. Example of when to use the Pythagorean Theorem: What is the length of the missing side? 64 in ? 18 in a² + b² = c²

  13. What is the difference between these two triangles?: 45º 45º You know EXACTLY what the angles are on the triangle on the LEFT. You DON’T KNOW EXACTLY what the angles are on the triangle on the RIGHT.

  14. Opposite Operations: X   X +- - + C²   c² Opposite Opposite Opposite Opposite Opposite Opposite

  15. 45 45 90 Special Right Triangle:

  16. 30 60 90 Special Right Triangle:

  17. Practice Problem#1: 45º x√2 x 45º x

  18. Practice Problem#1: 60º 2y y 30º y√3

  19. Practice Problem #1 What is the length of the missing side? a² + b² = c²

  20. Practice Problem #1 What is the length of the missing side? ? 10 in 14 in a² + b² = c²

  21. Template: Solving for c a² + b² = c² ( )( ) + ( )( ) = c² ( ) + ( ) = c² ( ) = c² √( ) = c = c

  22. Template: Solving for a or b a² + b² = c² a²+ ( )( ) = ( )( ) a² + ( ) = ( ) - ( )- ( ) a² = ( ) a = √( ) a =

  23. Pythagorean Theorem OR Special Right Triangles? 45º ? ? 4in 4in 45º 8in ? Special Right Triangles a² + b² = c²

  24. Practice Problem #1 What is the length of the missing side? a² + b² = c² OR Special Right Triangles?

  25. MCAS PROBLEM EXAMPLE: T X 6 in 45º W V 4 in Y

  26. MCAS PROBLEM EXAMPLE: T X 6 in 45º W V 4 in Y

  27. MCAS PROBLEM EXAMPLE: T X 6 in 45º Y W 4 in V

  28. T MCAS PROBLEM EXAMPLE: 6 in X 45º V W 4 in Y

  29. When you know the WHOLE and you know a PART, how do you find out what the UNKNOWN PART is? WHOLE -PART UNKNOWN PART