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Math Help - Related Rates Problem

  1. #1
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    Related Rates Problem

    Let ABC be a right triangle with fixed hypotenuse, c= 10 inches. If x (the angle at vertex A) is increasing at a rate of 4pi radians/min, find the rate at which a (the side opposite A) is increasing at the instant that x = pi/3 radians.

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  2. #2
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    Here's some hints

    \displaystyle \frac{dx}{dt} = 4\pi

    \displaystyle\sin x = \frac{a}{10} \implies a = 10\sin x then \displaystyle\frac{da}{dx} = 10\cos x
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  3. #3
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    And you want to evaluate \displaystyle \frac{da}{dt} = \frac{dx}{dt}\,\frac{da}{dx} at the point where \displaystyle x = \frac{\pi}{3}.
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