Question

A 5ft tall person is walking away from a 17ft tall lamppost at a rate of 6ft/sec. The scenario can be modeled with right triangles. At what rate is the length of the person's shadow changing when the person is 16ft from the lamppost?

Answer 1

you can use
\[\frac{17}{5}=\frac{x+y}{y}\]

Answer 2

this gives you a nice linear relation between \(x\) and \(y\) namely
\[12y=5x\]

Answer 3

since it is linear, the 16 part is unimportant
since you have
\[y=\frac{5}{12}x\] you know \[y'=\frac{5}{12}x'\] and you also know \(x'=6\) so you get
\[y'=\frac{30}{12}=\frac{5}{2}=2.5\]

Answer 4

GAH. I drew my triangles wrong. Thanks! You're always such a great help.
P.S. This is how I drew them XD