Question

A student who is 5 1/4 feet tall has a shadow that is 2 feet and 10 1/2 inches long. At the same time. a flag pole has a shadow that is 10 1/2 feel long. How tall, to the nearest inch, is the flag pole?

Answer 1

The height of the flag pole is approximately 19 feet and 2 inches.

Explanation:

Let suppose that length of the shadow of the object is directly proportional to its height. Hence:

`l \propto h`

`l = k\cdot h`

Where:

`h` - Height of the object, measured in inches.

`l` - Shadow length of the object, measured in inches.

`k` - Proportionality constant, dimensionless.

Now, let is find the value of the proportionality constant: (
`h = 5\,(1)/(4) \,ft` and
`l = 2\,ft\,\,10\,(1)/(2)\,in`)

`h = (21)/(4)\,ft`

`h = \left((21)/(4)\,ft \right)\cdot \left(12\,(in)/(ft) \right)`

`h = 63\,in`

`l = (2\,ft)\cdot \left(12\,(in)/(ft) \right) + (21)/(2)\,in`

`l = 24\,in + (21)/(2)\,in`

`l = (48)/(2)\,in+(21)/(2)\,in`

`l = (69)/(2)\,in`

Then,

`k = (l)/(h)`

`k = ((69)/(2)\,in )/(63\,in)`

`k = (69)/(126)`

`k = (23)/(42)`

The equation is represented by
`l = (23)/(42)\cdot h`. If
`l = 10\,(1)/(2)\,ft`, then:

`l = (21)/(2)\,ft`

`l = \left((21)/(2)\,ft \right)\cdot \left(12\,(in)/(ft) \right)`

`l = 126\,in`

The height of the flag pole is: (
`l = 126\,in`,
`k = (23)/(42)`)

`h = (l)/(k)`

`h = (126\,in)/((23)/(42) )`

`h = (5292)/(23)\,in`

`h = 230\,(2)/(23)\,in`

`h = (115)/(6)\,ft\,(2)/(23)\,in`

`h = 19\,(1)/(6)\,ft \,(2)/(23)\,in`

`h = 19\,ft\,\,2\,(2)/(23)\,in`

`h = 19\,ft\,\,2\,in`

The height of the flag pole is approximately 19 feet and 2 inches.