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anonymous

  • one year ago

i will medal anyone who helps please.its geometry Using the Tangent ratio, find BC, the height off the ground where the plank touches the wall. Round to the nearest tenth of a foot. (10 points)

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  1. anonymous
    • one year ago
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    just the second question please

  2. mathstudent55
    • one year ago
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    The problem does tell you to use the tangent ratio. Do you know what the tangent is equal to? It is the ratio of the length of which sides of a right triangle?

  3. anonymous
    • one year ago
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    i dont know what its equal to no

  4. mathstudent55
    • one year ago
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    |dw:1434492045351:dw|

  5. mathstudent55
    • one year ago
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    Look in the figure above. The since, cosine, and tangent are defined according to triangle side length ratios. The way to remember is SOHCAHTOA SOH: sine = opp/hyp CAH: cosine = adj/hyp TOA: tangent = opp/adj

  6. mathstudent55
    • one year ago
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    Ok. We see that the tangent ratio is the ratio of the lengths of the opposite leg to the adjacent leg.

  7. mathstudent55
    • one year ago
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    Now look in the figure with your problem. For angle C, whose measure we know, which side is the adjacent leg?

  8. anonymous
    • one year ago
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    im still really confused

  9. mathstudent55
    • one year ago
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    Do you need a more basic explanation? I can do it, I just need to find out how much I need to explain.

  10. anonymous
    • one year ago
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    lol very basic would help so much

  11. mathstudent55
    • one year ago
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    Ok. I will explain. Every time I post a response, read it, and respond ok for me to continue. The goal is for you to understand. Ok?

  12. anonymous
    • one year ago
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    ok

  13. mathstudent55
    • one year ago
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    A triangle has 3 sides. In the case of right triangle, two of the sides form a right angle. A right angle is an angle with a 90 degree measure.

  14. anonymous
    • one year ago
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    ok

  15. mathstudent55
    • one year ago
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    The three sides of a right triangles have names. The two sides that form the right angle are called "legs." The side opposite the right angle is called "hypotenuse." The hypotenuse is always the longest side of a right triangle.

  16. anonymous
    • one year ago
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    ok

  17. mathstudent55
    • one year ago
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    |dw:1434492764829:dw|

  18. mathstudent55
    • one year ago
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    The trigonometric ratios are ratios of lengths of sides of right triangles.

  19. mathstudent55
    • one year ago
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    The main three trig ratios are called: sine, cosine, and tangent.

  20. anonymous
    • one year ago
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    ok

  21. mathstudent55
    • one year ago
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    Ok?

  22. anonymous
    • one year ago
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    ok

  23. anonymous
    • one year ago
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    ?

  24. mathstudent55
    • one year ago
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    Look at the right triangle below. We are interested in angle A. |dw:1434493076172:dw|

  25. anonymous
    • one year ago
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    ok

  26. mathstudent55
    • one year ago
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    The sine ratio is defined as follows: \(\sin A = \dfrac{opposite ~leg}{hypotenuse}\)

  27. anonymous
    • one year ago
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    kk

  28. mathstudent55
    • one year ago
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    The sine of angle A is the ratio of the lengths of the opposite leg to the hypotenuse.

  29. anonymous
    • one year ago
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    k

  30. mathstudent55
    • one year ago
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    In a right triangle there is only one hypotenuse. When we say the hypotenuse, we know exactly which side we are referring to. In a right triangle, there are two legs. In general, the sides of right triangle that form the right angle are called just legs. In trig we need to distinguish between the legs, so we need to call the legs by different names to know which leg we are referring to.

  31. mathstudent55
    • one year ago
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    If you pick one of the acute angles of a right triangle, one leg is next to it. We call that leg the "adjacent leg" since adjacent means next to. That leg is next to that angle.

  32. anonymous
    • one year ago
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    k

  33. mathstudent55
    • one year ago
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    Once again, if you pick one of the acute angles of a right triangle, the other leg is across from that angle. We call that leg the opposite leg since opposite (in this case) means across from.

  34. anonymous
    • one year ago
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    ok so far im with you

  35. mathstudent55
    • one year ago
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    The figure below shows that for angle A, the opposite leg and the adjacent leg are positioned as labeled. |dw:1434493501483:dw|

  36. anonymous
    • one year ago
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    ok?

  37. mathstudent55
    • one year ago
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    Do you have a question?

  38. anonymous
    • one year ago
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    so far no

  39. mathstudent55
    • one year ago
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    Great. Let's continue.

  40. anonymous
    • one year ago
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    k

  41. mathstudent55
    • one year ago
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    If you use a scientific calculator, you can see that there are keys for sine, cosine, and tangent.

  42. anonymous
    • one year ago
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    k

  43. mathstudent55
    • one year ago
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    The values of the sine ratio, cosine ratio, and tangent ratio for all angles are known. Any calculator will tell you what they are.

  44. mathstudent55
    • one year ago
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    In trigonometry of right triangles, those same values of the the sin, cos, and tangent are ratios of lengths of sides of the right triangle.

  45. anonymous
    • one year ago
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    kk

  46. mathstudent55
    • one year ago
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    Now let's start with the sine ratio.

  47. mathstudent55
    • one year ago
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    The sine ratio is defined as the ratio of the lengths of the opposite leg to the hypotenuse. \(\sin A = \dfrac{opp}{hyp} \)

  48. mathstudent55
    • one year ago
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    Let's look at the following triangle and find the sine of A. |dw:1434493816047:dw|

  49. mathstudent55
    • one year ago
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    For angle A, the opposite leg is the one that measures 3 units. The hypotenuse measures 5 units. Since the sine ratio is defined as follows: \(\sin A = \dfrac{opp}{hyp} \) and we know the lengths of all the sides, we can find the sine of A.

  50. anonymous
    • one year ago
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    i think i have a guess on my answer real quick

  51. mathstudent55
    • one year ago
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    For our figure above, \(\sin A = \dfrac{opp}{hyp} = \dfrac{3}{5} = 0.6\)

  52. anonymous
    • one year ago
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    can i run an answer by you real quick?

  53. anonymous
    • one year ago
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    ???

  54. anonymous
    • one year ago
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    i believe the answer is about 3.6 but i need to put down how i got this answer

  55. mathstudent55
    • one year ago
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    Ok. Let's do the tangent ratio very quickly, then I'll show you how you use it.

  56. anonymous
    • one year ago
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    ok

  57. mathstudent55
    • one year ago
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    \(\tan A = \dfrac{opp}{adj} \)

  58. mathstudent55
    • one year ago
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    In our example above, the tangent of angle A is: \(\tan A = \dfrac{opp}{adj} = \dfrac{3}{4} = 0.75\)

  59. mathstudent55
    • one year ago
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    Now let's look at your problem.

  60. anonymous
    • one year ago
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    k

  61. mathstudent55
    • one year ago
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    |dw:1434494249181:dw|

  62. mathstudent55
    • one year ago
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    We need to use the tangent ratio to find BC, the left side of the triangle.

  63. mathstudent55
    • one year ago
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    The definition of the tangent ratio is: \(\tan C = \dfrac{opp}{adj} \)

  64. mathstudent55
    • one year ago
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    We look at angle C, and we decide which leg is adjacent and which leg is opposite.

  65. anonymous
    • one year ago
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    ok

  66. mathstudent55
    • one year ago
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    |dw:1434494411133:dw|

  67. anonymous
    • one year ago
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    ok

  68. mathstudent55
    • one year ago
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    Now using the definition of the tangent ratio, and the sides of the triangle, we can write the tangent of angle C. \(\tan C = \dfrac{opp}{adj} = \dfrac{3~ft}{BC} \) We know that angle C measures 49 deg. \(\tan 49^o = \dfrac{3}{BC} \)

  69. anonymous
    • one year ago
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    ok

  70. mathstudent55
    • one year ago
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    We want the length of BC. That is what we are trying to find. The tangent of 49 deg is simply a value that any scientific calculator can give you. We can solve the equation above for BC: \(\tan 49^o = \dfrac{3}{BC} \) \(BC \tan 49^o = 3\) \(BC = \dfrac{3}{\tan 49^o} \)

  71. mathstudent55
    • one year ago
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    Now use a calculator and divide 3 by tangent of 49 degrees.

  72. mathstudent55
    • one year ago
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    I get 1.1504 for tan of 49 deg, so 3/1.1504 = 2.607 That means BC = 2.6 ft

  73. anonymous
    • one year ago
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    ok

  74. anonymous
    • one year ago
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    thank you so much

  75. mathstudent55
    • one year ago
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    You are welcome.

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