Question

A yardstick casts a shadow of 24 in. at the same time a telephone pole casts a shadow of 20 ft 8 in. What is the height of the telephone pole, to the nearest inch?

Answer 1

The yardstick and its shadow form a right triangle that is similar to the right triangle formed by the telephone pole and its shadow, where the objects and their shadows correspond to one another, respectively.

This means there is some scale factor
`k` such that
`3k=x` where
`x` is the height of the telephone pole. (The 3 comes from the fact that you're using a yardstick, which is 3 feet long.)

Set up a proportion relation:


`\frac{\text{length of yardtick}}{\text{length of yardstick's shadow}}=\frac{\text{height of pole}}{\text{length of pole's shadow}}\iff\frac3{24}=\frac x{20+\frac8{12}}\implies x=(31)/(12)=2+\frac7{12}`

which means the telephone has a height of 12 ft 7 in.