use similar right triangles like this
![](http://img.sparknotes.com/figures/C/c92e38c46d6be4610999d7936fd45ce2/tree.gif)
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the bottom of the triangle will be described by 2 variables , s and one of your choice (i'll use x)
s for the distance from lamp to person
x as the distance from person to shadow's end
s+x is the whole bottom length of the lamp triangle
you know the height of the lamp and the person
set up similar triangles equation to solve for x (your shadow length)
take derivative and plug in ds/dt
This post was edited by saber_x3 on Mar 27 2014 12:05pm