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Math Help - Right angle evaluation problem, please help!

  1. #1
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    Right angle evaluation problem, please help!

    Hey,

    This question is from a college math placement practice test that I took yesterday and I couldnt for the life of me remember how to evaluate this angle.

    "In the right angle shown in the figure below, tan ( θ ) = _____ ?"
    Right angle evaluation problem, please help!-untitled.jpg

    it was multiple choice but I only have access to the question itself and the answer which i selected (randomly, may I add =p).

    Any help would be much appreciated, answer or otherwise, but i am most interested in the laws/formulas/ideas which allow you to evaluate this.

    Thanks a million for any help


    EDIT: the placement test is no calculator no notes, btw^^



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  2. #2
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    \tan(\theta)=\dfrac{\text{opp}}{\text{adj}}=\sqrt{  x^2-1}
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  3. #3
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    How did you get a value for the opposite side without adding another variable to the mix though?

    The furthest I can get without doing so is:

    cos θ = 1 / x

    tan θ = sin θ / cos θ = sin θ * x

    edit:

    The Law of Cosines!!

    Lol figured it out, thanks for the little push in that direction
    Last edited by brown399; August 2nd 2010 at 09:12 AM.
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  4. #4
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    The third side of that triangle is \sqrt{x^2-1}.
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  5. #5
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    Quote Originally Posted by brown399 View Post
    How did you get a value for the opposite side without adding another variable to the mix though?

    The furthest I can get without doing so is:

    cos θ = 1 / x

    tan θ = sin θ / cos θ = sin θ * x
    Pythagoras' theorem is one more way.

    Yet another way is

    cos^2\theta+sin^2\theta=1

    sin^2\theta=1-cos^2\theta

    sin\theta=\sqrt{1-cos^2\theta}

    tan\theta=\frac{sin\theta}{cos\theta}

    that can be simplified.
    Then you can also use trigonometric identities.
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