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Derivatives and rate of change

  1. Nov 3, 2013 #1
    1. A ladder 10 ft long rests against a vertical wall. Let θ be the angle between the top of the ladder and the wall and let x be the distance from the bottom of the ladder to the wall. If the
    bottom of the ladder slides away from the wall, how fast does x change with respect to θ when θ=[itex]\frac{∏}{3}[/itex]?



    2. Relevant equations

    The derivative rules.

    3. The attempt at a solution

    Using trig, I know the base of the triangle = 10sinθ)^2.

    Using the Pythagorean Theorem, I get the equation

    x^2=100-100sin^2θ

    x=√100(1-sin^2θ)

    What is my next step?
     
  2. jcsd
  3. Nov 3, 2013 #2
    Well, firstly you have your sines and cosines mixed up, the expression for [itex] x [/itex] should be,

    [itex] x = 10\sin\theta [/itex].

    Now that you have a functional relation between [itex] x [/itex] and [itex] \theta [/itex], what would the derivative of [itex] x [/itex] tell you?
     
  4. Nov 3, 2013 #3
    Ok I got it! I just drew my diagram wrong :P
     
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