A streetlight sits on top of a 20-foot pole. A six-foot tall man walks away from the pole at a rate of 5 ft/sec. At what rate is the man’s shadow growing when the man is 10 feet from the pole?

Step-by-step explanation:

We are given that

Height of pole,h=20 foot

Height of man,h'=6 foot

We have to find the rate at which the man's shadow growing when the man is 10 feet from the pole.

Let x be the distance of man from the pole and  y be the distance of tip of man's shadow from the pole.

Distance between man and shadow's tip=y-x

When two triangle are similar then the ratio of their corresponding sides are equal.

Differentiate w.r.t t

Hence, the man's shadow growing at rate when the man is 10 feet from the pole.