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A boat is observed from top of a $100\ \text m$ high cliff. The boat is travelling towards the cliff at a speed of $50\ \text{m/min}$. How fast is angle of depression changing when angle of depression is $15^\circ$. Give your answer to the nearest degree.

I differentiated $\theta$ with respect to time and got $\dfrac{-5000}{x^2 + 100^2}$ and substituted $x=\dfrac{100}{\tan15^\circ}$, but got the wrong answer.

Can someone please show me the correct steps?

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  • $\begingroup$ Is the answer 0.033 degrees/min? $\endgroup$ – Sudeepan Datta Jun 18 '14 at 12:59
  • $\begingroup$ The answer is 2 degrees/min , but I got 0.033 for some reason. $\endgroup$ – user155312 Jun 18 '14 at 13:00
  • $\begingroup$ Well, that's a pretty big difference... $\endgroup$ – Sudeepan Datta Jun 18 '14 at 13:06
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It looks as if you basically did it a correct way. But the answer you get out of the calculation is in radians per minute. Convert to degrees.

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