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anonymous

  • one year ago

Hi, this is my moms account I need help with a question I will fan and do a testimonial and best response if you help

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  1. anonymous
    • one year ago
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    In triangle DEF measurement angle D=45 degrees meausrement angle E=63 degrees and EF= 24 inches. What is DE to the nearest tenth of a inch

  2. anonymous
    • one year ago
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    there isnt a drawing

  3. Astrophysics
    • one year ago
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    |dw:1433827926366:dw| Hey so I think we can make a triangle as such, so we have an idea what we're looking for :)

  4. anonymous
    • one year ago
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    Okay so we are looking for x

  5. Astrophysics
    • one year ago
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    Yes, I just put a big question mark there instead so we know :), ok lets find the third angle first, and this seems like a sine law problem, so can you first tell me how many degrees are in a triangle?

  6. anonymous
    • one year ago
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    90

  7. Astrophysics
    • one year ago
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    Not quite, you may be thinking of a right triangle which is 90 degrees, but all triangles add up to 180, so our equation for the third angle would be as follow \[45 + 63 + x = 180 \]

  8. anonymous
    • one year ago
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    oh im sorry...so i would add 45 and 63 then subtract from 180?

  9. Astrophysics
    • one year ago
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    So just for convenience our third angle will be 72 degrees |dw:1433828380399:dw| ok so we have to use the sine law here, which can be used in any triangle where we have a side and its opposite angles, and yes!

  10. anonymous
    • one year ago
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    whats next?

  11. Astrophysics
    • one year ago
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    |dw:1433828458402:dw| \[\frac{ a }{ \sin(A) } = \frac{ b }{ \sin(B) }\] where A and B are known angles.

  12. Astrophysics
    • one year ago
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    Or we can use |dw:1433828607515:dw|

  13. Astrophysics
    • one year ago
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    \[\frac{ x }{ \sin(72) } = \frac{ 24 }{ \sin(63) }\] please check my work :)

  14. anonymous
    • one year ago
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    okay I get it so far

  15. anonymous
    • one year ago
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    why is it 72 and not 45?

  16. Astrophysics
    • one year ago
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    Now you just do the algebra for x, and we should get x!

  17. anonymous
    • one year ago
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    cross multiply...72 times 24 =63x?

  18. Astrophysics
    • one year ago
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    Because we need to find the length of a side, so we use the formula to find length on top, and we know the sin theta ratio.

  19. Astrophysics
    • one year ago
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    Yup, cross multiply works :) \[x \times \sin(63) = 24 \times \sin(72)\]

  20. anonymous
    • one year ago
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    sin 72 is .25382

  21. anonymous
    • one year ago
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    multiply that by 24?

  22. Astrophysics
    • one year ago
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    Yes

  23. anonymous
    • one year ago
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    6.0971

  24. Astrophysics
    • one year ago
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    Mhm, that does not look right

  25. Astrophysics
    • one year ago
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    sin(72) I got 0.95105...

  26. Astrophysics
    • one year ago
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    Make sure you're in degree mode on your calculator

  27. Astrophysics
    • one year ago
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    We should approximately get a length close to 24 (bit higher)

  28. Astrophysics
    • one year ago
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    for the final answer that is

  29. anonymous
    • one year ago
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    okay hold on

  30. Astrophysics
    • one year ago
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    Take your time :)

  31. anonymous
    • one year ago
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    22.825?

  32. anonymous
    • one year ago
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    @wolf1728 can you finish off?

  33. Astrophysics
    • one year ago
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    Ok now find x

  34. anonymous
    • one year ago
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    divide by sin 63?

  35. Astrophysics
    • one year ago
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    Good!

  36. anonymous
    • one year ago
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    I got .039

  37. anonymous
    • one year ago
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    my choices are 30.2 15.1 32.3 10.5

  38. anonymous
    • one year ago
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    I have to go soon and I have more questions to ask for tomorrow

  39. wolf1728
    • one year ago
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    I'm looking for the answers so far The angles are 45 63 and 72 and 1 side = 24

  40. anonymous
    • one year ago
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    correct thats what @Astrophysics and I got to

  41. wolf1728
    • one year ago
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    I calculate the other 2 sides as 19.047 and 25.617

  42. Astrophysics
    • one year ago
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    Yes, I got the same

  43. Astrophysics
    • one year ago
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    Maybe I made an error in the ratios, mhm...

  44. wolf1728
    • one year ago
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    Okay, then we're all set

  45. anonymous
    • one year ago
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    what is DE though?

  46. anonymous
    • one year ago
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    thats not an answer choice though

  47. Astrophysics
    • one year ago
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    Try 30.2

  48. wolf1728
    • one year ago
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    DE = 25.617 So, are the ONLY answers we can agree on are angles are 45 63 and 72 and 1 side = 24

  49. anonymous
    • one year ago
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    why 30.2?

  50. anonymous
    • one year ago
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    yes because 25 isnt a choice

  51. Astrophysics
    • one year ago
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    Yes, I'm getting the same answer, how many attempts do you have?

  52. anonymous
    • one year ago
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    just 1

  53. anonymous
    • one year ago
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    and 2 more kinda like it

  54. wolf1728
    • one year ago
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    I redrew the figure

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  55. anonymous
    • one year ago
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    what about the 63 degrees?

  56. Astrophysics
    • one year ago
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    Yes, that will work out much better!

  57. wolf1728
    • one year ago
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    Okay here's the NEW redrawn figure

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  58. anonymous
    • one year ago
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    okay now how do we use it to solve the problem

  59. Astrophysics
    • one year ago
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    So side a = 24, b = 32.2, and c = 30.24

  60. Astrophysics
    • one year ago
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    So 30.2 sounds about right, what do you think wolf?

  61. anonymous
    • one year ago
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    how did you get c=30.24?

  62. anonymous
    • one year ago
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    Im sorry im asking so much

  63. wolf1728
    • one year ago
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    I think the MAIN problem is interpreting the Law of Sines properly. We should agree on what exactly is angle A angle B angle C and side a side b side c

  64. anonymous
    • one year ago
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    alright we know that ef=24

  65. Astrophysics
    • one year ago
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    Ok, so lets use the original triangle |dw:1433831084347:dw|

  66. anonymous
    • one year ago
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    @wolf1728 do you agree so far?

  67. Astrophysics
    • one year ago
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    \[\frac{ a }{ \sin(a) } = \frac{ c }{ \sin(c) } \implies \frac{ 24 }{ \sin(45) } = \frac{ x }{ \sin(63) }\] \[\implies \frac{ 24 \sin(63) }{ \sin(45) } = x\]

  68. Astrophysics
    • one year ago
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    Sorry I misread my own triangle earlier haha.

  69. anonymous
    • one year ago
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    Oh so what I pointed out was right!

  70. anonymous
    • one year ago
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    lol

  71. wolf1728
    • one year ago
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    Okay I redrew it in terms of A B and C and sides a ,b and c

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  72. Astrophysics
    • one year ago
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    Now it should make sense, is that good @Miss.SweetiePie haha :)

  73. anonymous
    • one year ago
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    so we multiply sin 63 by 24?

  74. Astrophysics
    • one year ago
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    Yes

  75. anonymous
    • one year ago
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    .8910 is sin 63 now multiply by 24?

  76. wolf1728
    • one year ago
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    Astrophysics, you are stating that a/sin(A) = c/sin (C) we know angle A and angle C but we do NOT know side a or side c

  77. Astrophysics
    • one year ago
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    side a = 24

  78. wolf1728
    • one year ago
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    I'd say we should be interpreting the Law of Sines PRECISELY or else we'll get incorrect answers.

  79. anonymous
    • one year ago
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    So how do we do that

  80. Astrophysics
    • one year ago
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    I used my original triangle

  81. Astrophysics
    • one year ago
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    Only thing I didn't state was the angles, but those seem to be pretty obvious :P

  82. wolf1728
    • one year ago
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    Here is what I have for the Law of Sines:

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  83. anonymous
    • one year ago
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    I got 30.2 doing it that way

  84. Astrophysics
    • one year ago
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    Yes, I got the same

  85. anonymous
    • one year ago
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    what about you @wolf1728

  86. anonymous
    • one year ago
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    @Astrophysics and @wolf1728 can you help with 2 more and then ill give both of you testimonials and fan

  87. wolf1728
    • one year ago
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    I'm not sure. If you two agree then I'll say okay.

  88. wolf1728
    • one year ago
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    Heck, I'll help you out :-)

  89. anonymous
    • one year ago
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    thank you is it okay if I put it in here

  90. Astrophysics
    • one year ago
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    Haha, well this was all over the place, please open a new question @Miss.SweetiePie

  91. wolf1728
    • one year ago
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    sure - it's okay (I don;t need another medal)

  92. wolf1728
    • one year ago
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    Okay if you want a nice clean space then start a new question.

  93. Astrophysics
    • one year ago
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    Haha it's ok we can do it here, hey @Miss.SweetiePie was 30.2 right

  94. anonymous
    • one year ago
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    @Astrophysics is it okay to do one morein here then I open a new one?

  95. wolf1728
    • one year ago
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    go right ahead

  96. anonymous
    • one year ago
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    I'm not sure yet I havent sent it off

  97. Astrophysics
    • one year ago
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    I guess we should move on, before I start doubting myself :P

  98. anonymous
    • one year ago
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    Okay In triangle XYZ XY=13 YZ=20 and XZ=25 what is the measure of angle Z to the nearest degree

  99. anonymous
    • one year ago
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    what whats wrong

  100. Astrophysics
    • one year ago
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    Never mind lets ignore it haha

  101. Astrophysics
    • one year ago
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    I was just doubting

  102. anonymous
    • one year ago
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    lol okay...do you see the problem I just put up and please dont say that

  103. wolf1728
    • one year ago
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    I drew the diagram

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  104. Astrophysics
    • one year ago
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    |dw:1433832486973:dw|

  105. Astrophysics
    • one year ago
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    WE CAN USE COSINE LAW

  106. Astrophysics
    • one year ago
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    \[a^2=b^2+c^2 - 2bc \cos(A)\]

  107. anonymous
    • one year ago
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    okay so now we jus have to find angle z

  108. Astrophysics
    • one year ago
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    I think you should try to apply it now, and we'll just guide you :P, you have to learn this not us!

  109. anonymous
    • one year ago
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    13^2=20^2+25^2?

  110. wolf1728
    • one year ago
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    That is NOT a right triangle -(I think astrophysics knew that though)

  111. Astrophysics
    • one year ago
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    Yes, sorry the drawing should not be a right triangle, a bit more tilted

  112. wolf1728
    • one year ago
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    Okay - maybe we ALL knew that LOL

  113. anonymous
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    wait so what do I do? do I still do th 13^2 part

  114. Astrophysics
    • one year ago
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    Well first lets specify the angle|dw:1433832804456:dw|

  115. anonymous
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    thats the unknown angle

  116. wolf1728
    • one year ago
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    Here is what I have for Cosine Law

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  117. wolf1728
    • one year ago
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    We know all three sides so I think we have to use one of those formulas

  118. anonymous
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    Cos(C) ?

  119. Astrophysics
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    Yes, that's what we are looking for, that's for a triangle that looks as such |dw:1433832986527:dw| yes cos(C) looks good to me as well

  120. anonymous
    • one year ago
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    So a^2 would be j13^2?

  121. Astrophysics
    • one year ago
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    |dw:1433833163502:dw|

  122. wolf1728
    • one year ago
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    cosine (A) = [b^2 +c^2 - a^2] / (2*b*c) cosine (B) = [a^2 +c^2 - b^2] / (2*a*c) cosine (C) = [a^2 +b^2 - c^2] / (2*a*b)

  123. Astrophysics
    • one year ago
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    |dw:1433833225147:dw|

  124. Astrophysics
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    Now that's clear, at this point, we just plug and chug :P

  125. anonymous
    • one year ago
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    oh so a would be 25^2 correct?

  126. anonymous
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    b=20^2

  127. anonymous
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    minus 13^2?

  128. Astrophysics
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    Yeah

  129. anonymous
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    so 1025-169=856 but we have to find the sr

  130. Astrophysics
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    sr?

  131. Astrophysics
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    cosine (C) = [a^2 +b^2 - c^2] / (2*a*b)

  132. anonymous
    • one year ago
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    which is 29.25

  133. anonymous
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    so so far we have cos*C* 29.3/ 1000?

  134. Astrophysics
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    Not sure what you're doing, I did it all in one step

  135. Astrophysics
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    856 sounds good you need to divide by (2*a*b)

  136. Astrophysics
    • one year ago
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    Then we can find angle z

  137. anonymous
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    so 856/1000?

  138. Astrophysics
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    Yes now find the angle

  139. Astrophysics
    • one year ago
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    \[\cos(c) = .856\] do you know how to find angle c?

  140. Astrophysics
    • one year ago
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    You have to take the inverse

  141. Astrophysics
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    \[c = \cos^{-1} (0.856)\]

  142. wolf1728
    • one year ago
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    cosine (C) = [a^2 +b^2 - c^2] / (2*a*b) cosine (C) = [25^2 + 20^2 -13^2] / 2*25*20 cosine (C) = [625 + 400 -169] / 1,000 cosine (C) = 856 / 1,000 cosine (C) = .856 Arc cosine (.856) = 31.13 degrees

  143. anonymous
    • one year ago
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    inverse that okay let me calculatw

  144. Astrophysics
    • one year ago
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    Haha, right on wolf :)

  145. wolf1728
    • one year ago
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    Gee thanks :-)

  146. anonymous
    • one year ago
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    okay hold on please

  147. anonymous
    • one year ago
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    so thats it for that? nothing else?

  148. anonymous
    • one year ago
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    Im going to open up another question I have one more I think but can we go slow to make sure im still there

  149. anonymous
    • one year ago
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    understanding

  150. Astrophysics
    • one year ago
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    Yup, that's it to it :)

  151. wolf1728
    • one year ago
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    Need a good trigonometry calculator? Try this http://www.1728.org/trigcalc.htm

  152. Astrophysics
    • one year ago
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    The main thing is, you need to know how to set up the triangle

  153. wolf1728
    • one year ago
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    Absolutely, Astrophysics

  154. anonymous
    • one year ago
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    okay one more then I should be good...let me try to set it up in the enxt question please

  155. Astrophysics
    • one year ago
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    Go ahead :)

  156. wolf1728
    • one year ago
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    So, how about those Red Sox? LOL

  157. Astrophysics
    • one year ago
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    Haha, I wouldn't be sure, don't follow baseball, but I'm assuming there is a joke in there somewhere!

  158. wolf1728
    • one year ago
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    No I just typed something to fill in the space.

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spraguer (Moderator)
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is replying to Can someone tell me what button the professor is hitting...

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