Anna is 6 ft. tall. She is walking away from a street light that is 24 ft tall at a rate of 4 ft/sec. How fast is the length of her shadow changing?

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Answer 1 · 2016-11-04T14:16:09

$4/3$ ft/s

Let $A(t)$ be Anna position over time and $S_l(t)$ the lenght of Anna shadow over time.

$A^'(t)=4$

Using similar triangles

$(S_l(t)+A(t))/(S_l(t))=24/6 => S_l(t)+A(t) = 4S_l(t)=>S_l(t)=(A(t))/3$

$S_l^'(t)=(A^'(t))/3=4/3$