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Math Help - I am getting approximalte half what the answer should be (Related Rates Problem)

  1. #1
    s3a
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    I am getting approximalte half what the answer should be (Related Rates Problem)

    I am having trouble with this question but I believe it's a small mistake because I get approximately half of what the answer should be. I attached my work.

    Question: "A ladder 10 ft long leans against a vertical wall. If the bottom of the ladder slides away from the base of the wall at a speed of 2 ft/s, how fast is the angle between the ladder and the wall changing when the bottom of the ladder is 6ft from the base of the wall?

    Answer: 1/4 rad/s

    Any help would be greatly appreciated!
    Thanks in advance!
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    Quote Originally Posted by s3a View Post
    I am having trouble with this question but I believe it's a small mistake because I get approximately half of what the answer should be. I attached my work.

    Question: "A ladder 10 ft long leans against a vertical wall. If the bottom of the ladder slides away from the base of the wall at a speed of 2 ft/s, how fast is the angle between the ladder and the wall changing when the bottom of the ladder is 6ft from the base of the wall?

    Answer: 1/4 rad/s

    Any help would be greatly appreciated!
    Thanks in advance!
    let \theta = angle between the ladder and the wall

    \sin{\theta} = \frac{x}{10}

    \cos{\theta} \cdot \frac{d\theta}{dt} = \frac{1}{10} \cdot \frac{dx}{dt}

    \frac{8}{10} \cdot \frac{d\theta}{dt} = \frac{2}{10}

    \frac{d\theta}{dt} = \frac{2}{10} \cdot \frac{10}{8} = \frac{1}{4} rad/s
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  3. #3
    s3a
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    So my mistake was that SINE is what determines "THE ANGLE BETWEEN THE LADDER AND THE WALL?" Also, I now see the ladder is a constant and the x is not. Thanks.
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    Quote Originally Posted by s3a View Post
    So my mistake was that SINE is what determines "THE ANGLE BETWEEN THE LADDER AND THE WALL?"
    I don't know ... I don't do downloads on public message forums anymore.
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  5. #5
    s3a
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    Oh, well thanks still but if you didn't know, choosing to open rather than save pdf files would just store them into the hard drive temporarily.
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