I know this should be simple, but I still got it wrong... Another related rates, implicit differentiation problem: The base x of the right triangle below increases at a rate of 5 cm/s, while the height remains constant at h = 20. How fast is the angle θ changing when x = 20? I'll post diagrams and formulas for what I attempted to setup.

Question

anonymous · Answer

$$\tan \theta=20/x$$ then implicitly differentiated.

anonymous · Answer

I get $$\sec^2(\theta)*d \theta/dt =-20(dx/dt)/x^2$$ solve for theta rate of change

anonymous · Answer

I got $$-20(dx/dt)\cos^2\theta/x^2$$ because 1/sec^2 is cos^2? I hope.... am I starting completely wrong? have I missed a sign somewhere?

anonymous · Answer

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Am I assuming the right angle $\theta$?

anonymous · Answer

yes, sorry.... forgot to post that.

anonymous · Answer

I think you're doing great so far. All you need now is to substitute in the equation you've got for the rate of change.

anonymous · Answer

You're right I found it.... I just multiplied wrong... I couldn't figure out why it wasn't coming out right and I doubted I had started right because of the sec^2 to cos^2....
yes, I have it now.

anonymous · Answer

Good!

anonymous · Answer

thank you... now to the last two problems... see if I can solve them myself first...