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Math Help - Slidding ladder calculous problem

  1. #1
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    Slidding ladder calculous problem

    A 25 ft ladder is leaning against a house when its base starts to slide away. By the time the base is 7 ft from the house, the base is moving away at the rate of 24 ft/sec
    a. what is the rate of change of the height of the top of the ladder?
    b. at what rate is the area of the triangle formed by the ladder, wall, and ground changing then?
    c. at what rate is the angle between the ladder and the ground changing then?
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  2. #2
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    Re: Slidding ladder calculous problem

    Denote the base and height of the ladder by b and h, such that b^2 + h^2 = 25^2. Differentiating both sides with respect to t,

    2b \frac{db}{dt} + 2h \frac{dh}{dt} = 0

    For part a, you already know what db/dt is, as well as b and h at this moment in time. Here it is easy to find dh/dt.
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