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Math Help - Related rates problem

  1. #1
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    Related rates problem

    A plane flies horizontally at an altitude of 5 km and passes directly over a tracking telescope on the ground. When the angle of elevation is is pi/3, this angle is decreasing at a rate of pi/6 rad/min. How fast is the plane travelling at that time?



    Now I need to find 'y' which is impossible because I only have one given side and one angle. How do I solve the rest?
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  2. #2
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    Re: Related rates problem

    Also I forgot to add in the Chain Rule for the differentiation, so there should be a dtheta/dt added onto that second term. But we already know that value so the problem is still finding the y.
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  3. #3
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    Re: Related rates problem

    \cot{\theta} = \frac{y}{5}

    -\csc^2{\theta} \cdot \frac{d\theta}{dt} = \frac{1}{5} \cdot \frac{dy}{dt}

    -5\csc^2{\theta} \cdot \frac{d\theta}{dt} = \frac{dy}{dt}

    plug and chug the left side and evaluate \frac{dy}{dt}
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