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Math Help - Word problem

  1. #1
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    Word problem

    Here's my problem...

    A street light is at the top of a ft. tall pole. A man ft tall walks away from the pole with a speed of feet/sec along a straight path. How fast is the tip of his shadow moving away from the pole when the man is feet from the pole?

    Any suggestions on how to start out?
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  2. #2
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    Absolutely! Draw some similar triangles. One has height of the flag pols. The other has height of the man.

    Let's see what you get.
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  3. #3
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    So I've drawn my similar triangles. I guess my question would be how do I relate the two to arrive at my answer. In other words, do I need to find the hypotenuse of the triangle with the height of the pole?
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  4. #4
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    Stuff we know...

    x = the distance from the pole to the guy.

    y = the length of the guy's shadow

    p = height of pole

    g = height of guy

    Now, what do similar triangles do for us?

    p/g = (x+y)/y
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  5. #5
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    The ratio of their corresponding sides are similar.

    so
    x=44 ft
    y=?
    p=10.5ft
    g=5.9ft

    so to find y, plug in all the variables into the equation below? The problem is tough for me to comprehend because we're finding how fast his shadow is moving away from the pole but do we just assume the sun is in a certain location to give us the needed length of his shadow?
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  6. #6
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    You DO have to figure out that x = x(t) and y = y(t). The other two are constants.
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