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Unit 2 - Right Triangles and Trigonometry

Unit 2 - Right Triangles and Trigonometry. Chapter 8. Triangle Inequality Theorem. Need to know if a set of numbers can actually form a triangle before you classify it. Triangle Inequality Theorem: The sum of any two sides must be larger than the third. Example: 5, 6, 7

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Unit 2 - Right Triangles and Trigonometry

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  1. Unit 2 - Right Triangles and Trigonometry Chapter 8

  2. Triangle Inequality Theorem • Need to know if a set of numbers can actually form a triangle before you classify it. • Triangle Inequality Theorem: The sum of any two sides must be larger than the third. • Example: 5, 6, 7 • Since 5+6 > 7 6+7 > 5 5+7 > 6 it is a triangle • Example: 1, 2, 3 • Since 1+2 = 3 2+3 > 1 3+1 > 2 it is not a triangle!

  3. Examples - Converse • Can this form a triangle? • Prove it: Show the work! • Can this form a triangle? • Prove it: Show the Work!

  4. Pythagorean Theorem and Its Converse • Pythagorean Theorem c a b • Converse of the Pythagorean Theorem • c2 < a2 + b2 then Acute • c2 = a2 + b2 then Right • c2 > a2 + b2 then Obtuse

  5. Examples – What type of triangle am I? • . • . 3. 4.

  6. Pythagorean Triple • A set of nonzero whole numbers a, b, and c that satisfy the equation • Common Triples • 3, 4, 5 • 5, 12, 13 • 8, 15, 17 • 7, 24, 25 • They can also be multiples of the common triples such as: • 6, 8, 10 • 9, 12, 15 • 15, 20, 25 • 14, 28, 50

  7. Section 8.2 Special Right Triangles

  8. Special Right Triangles • 45°-45°-90° x x

  9. Examples – Solve for the Missing Sides • Solve or x and y • Solve for e and f

  10. Special Right Triangles • 30°-60°-90° 2x x

  11. Examples – Solve for the Missing Sides • Solve for x and y • Solve for x and y

  12. Section 8.3 Right Triangle Trigonometry

  13. Trigonometric Ratios • Sine = Opposite Hypotenuse • Cosine = Adjacent Hypotenuse • Tangent = Opposite Adjacent

  14. SOHCAHTOARemember this!!!!Write this on the top of your paper on all tests and homework!

  15. Set up the problem • Sin • Cos • Tan • Sin • Cos • Tan

  16. Set up the problem • Sin • Cos • Tan

  17. Trigonometric Ratios: • When you have the angle you would use: • When you need the angle you would use:

  18. Examples • Solve for the missing variable • Solve for the missing variable

  19. Examples • Solve for the missing variable • Solve for the missing variable

  20. Examples • Find m< A and m< B

  21. Examples • Solve for the missing variables

  22. Section 8.4 Angle of Elevation and Angle of Depression

  23. Elevation verse Depression – Point of View • Angle of Elevation • Angle of Depression

  24. Examples – Point of View • Elevation • Depression

  25. Examples – Point of View • Find the Angle Elevation • Find the Height of the boat from the sea floor.

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