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Right Triangles

Right Triangles. The Trig Ratios. Brought to you by Moody Mathematics. Let’s review some vocabulary. Moody Mathematics. A. Hypotenuse. C. B. Moody Mathematics. Opposite Leg. A. C. B. Opposite Leg to A. Moody Mathematics. Opposite Leg. Opposite Leg to B. B. Moody Mathematics. A.

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Right Triangles

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  1. Right Triangles The Trig Ratios Brought to you by Moody Mathematics

  2. Let’s review some vocabulary. Moody Mathematics

  3. A Hypotenuse C B Moody Mathematics

  4. Opposite Leg A C B Opposite Leg to A Moody Mathematics

  5. Opposite Leg Opposite Leg to B B Moody Mathematics

  6. A Adjacent Leg Adjacent Leg to A B Moody Mathematics

  7. Adjacent Leg B Adjacent Leg to B Moody Mathematics

  8. Consider the right triangles in this next slide: Moody Mathematics

  9. What can you say about them? Moody Mathematics

  10. They are similar By AA Moody Mathematics

  11. They have the same right angle They have the same acute angle Moody Mathematics

  12. All right triangles having one acute angle the same are similar. Moody Mathematics

  13. For example, all 45-45-90 triangles are similar. Moody Mathematics

  14. The legs of a 45-45-90 triangle are in a 1 to 1 ratio. Moody Mathematics

  15. In a 45-45-90 triangle the ratio: leg hypotenuse Moody Mathematics

  16. Also, all 30-60-90 triangles are similar. Moody Mathematics

  17. In a 30-60-90 triangle, the ratio: leg opposite the 30o hypotenuse Moody Mathematics

  18. The ratio: leg opposite the 600 hypotenuse Moody Mathematics

  19. We have names for the 3 most common ratios that we will form in right triangles. Moody Mathematics

  20. The names are: the Sine Ratio, the Cosine Ratio, the Tangent Ratio. Moody Mathematics

  21. Sin A= Cos A= Tan A= Moody Mathematics

  22. S O H – C A H – T O A “Some Old Hippy Caught Another Hippy Tripping On Antacid” Moody Mathematics

  23. in SOH pposite ypotenuse Moody Mathematics

  24. os CAH djacent ypotenuse Moody Mathematics

  25. an TOA pposite djacent Moody Mathematics

  26. Sin A = A Hypotenuse C B Opposite Leg to A Moody Mathematics

  27. A Cos A = Hypotenuse Adjacent Leg to A B C Moody Mathematics

  28. A Tan A= Adjacent Leg to A B Opposite Leg to A C Moody Mathematics

  29. Now let’s set up the three ratios for angle B. Moody Mathematics

  30. A Sin B= Hypotenuse Opposite Leg to B B C Moody Mathematics

  31. Cos B = A Hypotenuse C B Adjacent Leg to B Moody Mathematics

  32. A Tan B = Opposite Leg to B B Adjacent Leg to B C Moody Mathematics

  33. Now let’s use a ratio to solve for a missing side of a right triangle: Moody Mathematics

  34. Let’s estimate the value of x before we start: a. X>12 b. 6<x<12 c. X<6 A C B Moody Mathematics

  35. It’s not (a) because A leg can’t be longer than the hypotenuse. a. X>12 b. 6<x<12 c. X<6 A C B Moody Mathematics

  36. If B were 30o then x would be 6 exactly. Since B is smaller than 30o x<6. b. 6<x<12 c. X<6 A C B Moody Mathematics

  37. Look at the parts involved and decide which ratio “fits” best. A C B Moody Mathematics

  38. Where are the given and missing sides in relation to the known angle? A C B Moody Mathematics

  39. X is the “opposite leg” to B and 12 is the “hypotenuse”. A C B Moody Mathematics

  40. A C B Moody Mathematics

  41. Now let’s use another ratio to solve for a missing side of a right triangle: Moody Mathematics

  42. Let’s estimate the value of x before we start: a. X>16 b. 8<x<16 c. X<8 A B C Moody Mathematics

  43. It’s not (a) because A leg can’t be longer than the hypotenuse. a. X>16 b. 8<x<16 c. X<8 A B C Moody Mathematics

  44. If A were 30o then x would be 8. Since <A =55o is bigger than30o, x>8. b. 8<x<16 c. X<8 A B C Moody Mathematics

  45. Look at the parts involved and decide which ratio “fits” best. A B C Moody Mathematics

  46. Where are the given and missing sides in relation to the known angle? A B C Moody Mathematics

  47. X is the “adjacent leg” to B and 16 is the “hypotenuse”. A B C Moody Mathematics

  48. A B C Moody Mathematics

  49. Now let’s solve another ratio to find a missing side of a right triangle, but this time x is on the bottom. Moody Mathematics

  50. Look at the parts involved and decide which ratio “fits” best. A B C Moody Mathematics

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