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Math Help - Find Rate of Change of Angle

  1. #1
    Senior Member nycmath's Avatar
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    Find Rate of Change of Angle

    A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 2ft per second. Find the rate at which the angle between the ladder and the wall of the house is changing when the base of the ladder is 7 feet from the wall.

    My Set Up:

    tan(theta) = 7/x

    Is that the correct trig equation?
    I took the implicit derivative of both sides but ended up with a
    sec^2 (theta) function that led to the wrong answer.

    The book does not explain how to find angles in terms of related rates. How is this done? I will then use your steps to solve similar questions. Thank you.
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  2. #2
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    Re: Find Rate of Change of Angle

    Quote Originally Posted by nycmath View Post
    A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 2ft per second. Find the rate at which the angle between the ladder and the wall of the house is changing when the base of the ladder is 7 feet from the wall.

    My Set Up:

    tan(theta) = 7/x

    Is that the correct trig equation?
    It's impossible to say without knowing what "theta" and "x" are intended to mean!
    If theta is "the angle between the ladder and the wall of the house" and x is the distance from the wall to the foot of the house, then, yes it is.

    I took the implicit derivative of both sides but ended up with a
    sec^2 (theta) function that led to the wrong answer.

    The book does not explain how to find angles in terms of related rates. How is this done? I will then use your steps to solve similar questions. Thank you.
    What equation did you get and what "wrong answer" did you get?
    Thanks from nycmath
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  3. #3
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    Re: Find Rate of Change of Angle

    Find Rate of Change of Angle-20-nov-13.png
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  4. #4
    Senior Member nycmath's Avatar
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    Re: Find Rate of Change of Angle

    I move on from chapter to chapter in my single variable textbook after getting more questions right than wrong at the end of each chapter section. I did fairly well in terms of related rates. Considering that I am not in a formal calculus 1 course helps me avoid anxiety. I will return to related rates in the near future. I am learning calculus on my own. I find this subject most interesting. Of course, I will never uunderstand it as well as a math major but I am not competing with anyone. I am simply having fun with math. I am now studying extrema.In fact, I have some extrema questions that I will post later today. Thanks for all your help.
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