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Trigonometry 3d pyramid question

  1. May 11, 2013 #1
    1. The problem statement, all variables and given/known data

    http://imgur.com/x8D2wqO

    I need to solve for theta and I keep getting the angle 65, using cosine law and pythagorean theorem but the answer key says that the angle is 93. The diagram is not to scale. Is my answer wrong or is the answer key incorrect?
     
  2. jcsd
  3. May 11, 2013 #2

    haruspex

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    It isn't quite clear what length is 15cm. Is it AC or AD? To get 93 degrees, it would probably have to be AC. Either way, there does not seem to be enough information. Please post your working.
     
  4. May 11, 2013 #3
    15 cm is AD
     
  5. May 11, 2013 #4
    c^2 = a^2 + b^2 - 2abcosC
    c = 23.7471

    h^2 = a^2 + b^2
    h = 23.4307

    h^2 = a^2 + b^2
    h = 20.5183

    (23.7471)^2 = (23.4307)^2 + (20.5183)^2 - 2(23.4307)(20.5183)costheta
    theta = 65
     
  6. May 11, 2013 #5

    haruspex

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    I can't be expected to follow that if you keep changing what the letters refer to and don't specify each time.
     
  7. May 11, 2013 #6
    Using AD = 15cm, BD = 18cm, CD = 14cm and angle BDC = 95 degrees, I too get 65 degrees as angle BAC.
     
  8. May 11, 2013 #7
    c^2 = a^2 + b^2 - 2abcosC
    c = 23.7471 Finding length of BC

    h^2 = a^2 + b^2
    h = 23.4307 Finding length of AB

    h^2 = a^2 + b^2
    h = 20.5183 Finding length of AC

    (23.7471)^2 = (23.4307)^2 + (20.5183)^2 - 2(23.4307)(20.5183)costheta
    theta = 65 Finding angle theta of triangle ABC
     
  9. May 12, 2013 #8

    haruspex

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    After making some guesses about the other assignments in those equations, I'm led to suppose you are taking angles ADB, ADC to be right angles. I don't see that stated anywhere.
    As I said, to get an angle of over 90 degrees as the answer, you will need the 15cm to refer to AC, not AD. OTOH, I then get 91.9 degrees, so it still doesn't seem quite right.
     
  10. May 12, 2013 #9
    All right so it must be a textbook answer key problem. Thank you very much for your help
     
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