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Math Help - Triangle dz/dt question

  1. #1
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    Triangle dz/dt question

    The sides of a right triangle are x, y, and z with z being the hypoteneuse. If the sides are increasing in such a way that dz/dt = 1, dx/dt = 3dy/dt, find dy/dt at the instant x = 12 and y = 5.

    I know that z = 13 according to the Pythagorean Theorem, but beyond that I do not know what to do. I guess my problem is I do not understand how derivatives relate to the sides of a triangle. I've only used them with functions before.

    Please help!
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  2. #2
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by poitier View Post
    The sides of a right triangle are x, y, and z with z being the hypoteneuse. If the sides are increasing in such a way that dz/dt = 1, dx/dt = 3dy/dt, find dy/dt at the instant x = 12 and y = 5.

    I know that z = 13 according to the Pythagorean Theorem, but beyond that I do not know what to do. I guess my problem is I do not understand how derivatives relate to the sides of a triangle. I've only used them with functions before.

    Please help!
    by Pythagorean theorem

    z^2 = x^2 + y^2 derive it

    2 z \frac{dz}{dt} = 2 x \frac{dx}{dt} + 2 y \frac{dy}{dt}

    dz/dt , dx/dt , x ,y these things are given you find z =13 sub these to what I get to find dy/dt
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  3. #3
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    Thank you! That makes sense.
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