Related Rates: Shadow Problem with Moving Object

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Homework Statement


A spotlight on theground shines on a wall 12 m away. If a man 2m tall walks from the spotlight toward the building at a speed of 1.6m/s. how fast is the length of his shadow on the building decreasing when he is 4m from the building?

The Attempt at a Solution



x=4m dx/dt=1.6m/s dy/dt=?

I am kinda of stuck on this one. I know that as x decreases z and y will also decrease. But I am really not to sure how to proceed on this one any hints?
 
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You need a relation between x, the distance from the wall and y, the height of the shadow. Draw a picture and find two similar triangles.
 
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There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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