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Math Help - Related Rates Similar Triangles

  1. #1
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    Related Rates Similar Triangles

    While in Wonderland, Alice eats a cookie that makes her grow taller at a rate of 0.5 ft/min. She is standing 40 feet away from a light which is 20 feet tall. How fast is the length of her shadow changing when she is 15 feet tall?

    I know that this is a similar triangles problem and you have to cross-multiply the ratios, but that's all that I know. Can someone please help me? Thank you so much!
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  2. #2
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    Let "x" be Alice's height and "y" be the length of her shadow. Then using similar triangles, as you say, should give \frac{y}{x}= \frac{y+ 40}{20}. "Cross multiplying" you get 20y= x(y+ 40).

    Now differentiate both sides with respect to time, "t", to get an equation relating \frac{dx}{dt} and \frac{dy}{dt}. You are told that \frac{dx}{dt}= 0.5 and are asked to find \frac{dy}{dt} when y= 15.
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  3. #3
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    Wow, you make it so simple! All my friends complicated it and just confused me even more. Thank you so much, you have no idea.. you saved my life lol!
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