Question

A telephone pole has a shadow of 16 ft. when a person 5 ft. tall has a shadow of 6 ft. How tall is the pole?

Write answer to nearest tenth or as a fraction.
x = ft.

Answer 1

`The\ height\ of\ the\ poll\ is\ (40)/(3)\ ft\ and\ 13.3\ ft .`

Explanation:

Let us assume that the Height of an object be h.

Let us assume that the shadow of an object be y.

(As shadow is always proportional to height .)

Thus

`y \propto h`

y = kh

As given

when a person 5 ft. tall has a shadow of 6 ft.

h = 5 ft and y = 6 ft

Put in y = kh

6 = 5k

`k = (6)/(5)`

As given

A telephone pole has a shadow of 16 ft.

Let us assume that the height of the pole be x.

h = x and y = 16 ft

16 = hk

`k = (16)/(x)`

Compare the value of k.

`(6)/(5) = (16)/(x)`

`x = (16* 5)/(6)`

`x = (80)/(6)`

`x = (40)/(3)\ ft`

or

x = 13.3 ft

`Therefore\ the\ height\ of\ the\ poll\ is\ (40)/(3)\ ft\ and\ 13.3\ ft .`

Answer 2

it should have to be 13.3