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anonymous

  • one year ago

Please help!

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  1. anonymous
    • one year ago
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  2. jim_thompson5910
    • one year ago
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    Start by drawing any generic triangle ABC |dw:1434070079074:dw|

  3. jim_thompson5910
    • one year ago
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    A = 43 degrees B = 62 degrees we can find C A+B+C = 180 43+62+C = 180 C = 75 |dw:1434070139361:dw|

  4. jim_thompson5910
    • one year ago
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    yes, BC = 22 and AB = unknown Let x = AB |dw:1434070198509:dw|

  5. anonymous
    • one year ago
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    yes I know that much

  6. jim_thompson5910
    • one year ago
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    now you use the law of sines sin(A)/a = sin(C)/c sin(43)/22 = sin(75)/x solve for x

  7. anonymous
    • one year ago
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    \[\frac{ \sin43 }{ 22 } = \frac{ \sin75 }{ x }\]

  8. anonymous
    • one year ago
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    I'm honestly not sure how to solve for x @jim_thompson5910

  9. jim_thompson5910
    • one year ago
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    using a calculator, you should find that sin(75) = 0.96592582628907 sin(43) = 0.6819983600625

  10. jim_thompson5910
    • one year ago
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    replace sin(43) and sin(75) with those approx values cross multiply and then solve for x

  11. anonymous
    • one year ago
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    ooh ok thank you

  12. anonymous
    • one year ago
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    this is what I got...

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  13. jim_thompson5910
    • one year ago
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    you can also do it symbolically like this \[\Large \frac{\sin(43)}{22}=\frac{\sin(75)}{x}\] \[\Large \sin(43)*x=22*\sin(75)\] \[\Large x=\frac{22*\sin(75)}{\sin(43)}\] \[\Large x=???\] treating sin(43) and sin(75) as if they are variables

  14. jim_thompson5910
    • one year ago
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    desmos is in radian mode by default

  15. jim_thompson5910
    • one year ago
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    click the wrench icon and switch to degree mode

  16. anonymous
    • one year ago
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    Is there a place to put degrees in desmos?

  17. jim_thompson5910
    • one year ago
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    it's off to the right side

  18. anonymous
    • one year ago
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    oh thank you

  19. anonymous
    • one year ago
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    so the first one is D?

  20. jim_thompson5910
    • one year ago
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    yeah I get 31.1589725471071 which rounds to 31.2

  21. anonymous
    • one year ago
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    Thanks I think I can get the 2nd on my own

  22. jim_thompson5910
    • one year ago
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    np

  23. anonymous
    • one year ago
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    |dw:1434070810160:dw|

  24. anonymous
    • one year ago
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    |dw:1434070891025:dw|

  25. anonymous
    • one year ago
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    sorry I'm just using this to walk myself through it you can leave @jim_thompson5910

  26. jim_thompson5910
    • one year ago
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    alright, feel free to ask if you get stuck anywhere

  27. anonymous
    • one year ago
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    great I'm already stuck -.-

  28. anonymous
    • one year ago
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    I'm not sure what to use to find r... @jim_thompson5910

  29. jim_thompson5910
    • one year ago
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    you need qr to find r (with the law of sines) but before you can use the law of sines, you have to use the law of cosines to find qr

  30. anonymous
    • one year ago
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    ok...

  31. jim_thompson5910
    • one year ago
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    |dw:1434071160502:dw|

  32. anonymous
    • one year ago
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    \[c^{2} = 7.5^{2} + 8.4^{2} - 2(7.5)(8.4)\cos(43)\]

  33. anonymous
    • one year ago
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    like that?

  34. jim_thompson5910
    • one year ago
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    very good

  35. jim_thompson5910
    • one year ago
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    isolate c

  36. anonymous
    • one year ago
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    ok I'm working it out now...

  37. anonymous
    • one year ago
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    I got c = 7.54

  38. jim_thompson5910
    • one year ago
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    me too

  39. anonymous
    • one year ago
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    |dw:1434071506507:dw|

  40. jim_thompson5910
    • one year ago
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    now you can use the law of sines

  41. anonymous
    • one year ago
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    can you set it up for me like you did with the last one? I'm very bad at this...

  42. jim_thompson5910
    • one year ago
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    the law of sines works like this sin(A)/a = sin(B)/b = sin(C)/c |dw:1434071589360:dw|

  43. jim_thompson5910
    • one year ago
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    the letters pair up (upper and lower case) A pairs with a B with b C with c you'll have sin(A) pair with a, so that's how I got one fraction sin(A)/a same with sin(B)/b and sin(C)/c

  44. jim_thompson5910
    • one year ago
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    normally you don't know the full picture of the triangle so instead of saying sin(A)/a = sin(B)/b = sin(C)/c you would use sin(A)/a = sin(B)/b or sin(B)/b = sin(C)/c or sin(A)/a = sin(C)/c

  45. anonymous
    • one year ago
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    \[\frac{ \sin43 }{ 7.5 } = \frac{ \sin7.5 }{ x }\]

  46. anonymous
    • one year ago
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    so this works?

  47. jim_thompson5910
    • one year ago
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    I would use the full decimal expansion of qr instead of 7.5 or you can use a longer version, say qr = 7.5409365

  48. jim_thompson5910
    • one year ago
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    and the second fraction won't have sin(7.5)

  49. jim_thompson5910
    • one year ago
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    |dw:1434071876378:dw|

  50. jim_thompson5910
    • one year ago
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    |dw:1434071921347:dw|

  51. anonymous
    • one year ago
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    oh ok, so is this the right format (besides the larger decimal)?

  52. jim_thompson5910
    • one year ago
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    do you see how I have sin(r)/7.5 ?

  53. anonymous
    • one year ago
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    oooh ya I'll fix that

  54. anonymous
    • one year ago
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    \[7.5= \frac{ 7.5*\sin x }{ \sin 43 }\]

  55. anonymous
    • one year ago
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    I'm just screwing this up aren't I?

  56. jim_thompson5910
    • one year ago
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    you're doing great

  57. jim_thompson5910
    • one year ago
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    don't worry

  58. anonymous
    • one year ago
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    ok but how do I isolate x?

  59. jim_thompson5910
    • one year ago
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    First cross multiply. Then isolate sin(x). Finally use arcsine to fully isolate x \[\Large \frac{\sin(43)}{7.5409365}=\frac{\sin(x)}{7.5}\] \[\Large 7.5*\sin(43)=7.5409365*\sin(x)\] \[\Large 7.5409365*\sin(x) = 7.5*\sin(43)\] \[\Large \sin(x)=\frac{7.5*\sin(43)}{7.5409365}\] \[\Large x=???\]

  60. anonymous
    • one year ago
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    OOOH thank you so much!

  61. jim_thompson5910
    • one year ago
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    what result do you get

  62. anonymous
    • one year ago
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    um... I got lost after this far

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  63. anonymous
    • one year ago
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    I'm not sure what to do with the sin x to find x

  64. jim_thompson5910
    • one year ago
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    the top 7.5 should use more decimal digits (say 4 or 5)

  65. jim_thompson5910
    • one year ago
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    oops I meant the bottom 7.5

  66. anonymous
    • one year ago
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    didn't change much

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  67. jim_thompson5910
    • one year ago
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    oh wait, I just realized that qr isn't 7.5 you were in radian mode on accident (I was too)

  68. jim_thompson5910
    • one year ago
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    no wonder I'm not getting the answer choices

  69. anonymous
    • one year ago
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    woooow XD ok then what is it??

  70. jim_thompson5910
    • one year ago
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    this is the length of qr

  71. jim_thompson5910
    • one year ago
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    QR = 5.887226 approximately |dw:1434072742525:dw|

  72. anonymous
    • one year ago
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    here's what I got

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  73. jim_thompson5910
    • one year ago
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    \[\Large \frac{\sin(43)}{5.887226}=\frac{\sin(x)}{7.5}\] \[\Large 7.5*\sin(43)=5.887226*\sin(x)\] \[\Large 5.887226*\sin(x) = 7.5*\sin(43)\] \[\Large \sin(x)=\frac{7.5*\sin(43)}{5.887226}\] \[\Large x=???\]

  74. anonymous
    • one year ago
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    oh oops I changed the other 7.5 XD

  75. anonymous
    • one year ago
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    there we go!

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  76. jim_thompson5910
    • one year ago
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    now evaluate the arcsine of that number

  77. jim_thompson5910
    • one year ago
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  78. anonymous
    • one year ago
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    Ta Da!

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  79. jim_thompson5910
    • one year ago
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    you nailed it

  80. anonymous
    • one year ago
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    so its D?

  81. jim_thompson5910
    • one year ago
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    both seem to be D, yes I guess the makers weren't too creative

  82. anonymous
    • one year ago
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    haha well thank you SO much! *hugs*

  83. jim_thompson5910
    • one year ago
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    you're welcome

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