did you make your sketch?
in my picture, I let the length of the person's shadow be y , and the distance of the person form the post as x as suggested.
so by similar triangles,
5/y = 16/(x+y)
16y = 5x+5y
11y = 5x
11 dy/dt = 5 dx/dt
dy/dt = (5/11)(2/x) = 10/(11x)
this is the rate we want when x = 12
rate at which shadow is changing
= dy/dt
= 10/132
= 5/66 ft/s
Hello! I'm having trouble with this related rates problem: A 5ft tall person is walking away from a 16ft tall lamppost at a rate of (2/x) ft/sec, where x is the distance from the person to the lamppost. Assume the scenario can be modeled with right triangles. At what rate is the length of the person's shadow changing when the person is 12 ft from the lamppost?
The answer the teacher gave me is 5/66 ft/sec. I'm wondering how she got that answer??
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