Question

To find the height h of a flagpole, Casey measured her own shadow and the flagpole’s shadow. Given that Casey’s height is 5 feet 4 inches, what is the height of the flagpole?

Answer 1

The height of the flagpole is 25 feet 4 inches.

What is the height of the flagpole?

Casey shadow:

Base = 3 feet

Height = 5 feet 4 inches

Flagpole:

Base = 14 feet 3 inches

Height = h

Convert feet to inches:

1 feet = 12 inches

5 feet 4 inches = 64 inches

3 feet = 36 inches

14 feet 3 inches = 171 inches

So,

36 inches : 171 inches = 64 inches : h

36/171 = 64/h

cross product

36 × h = 171 × 64

36h = 10,944

h = 10,944/36

h = 304 inches

Therefore,

convert 304 inches to feet = 304/12

= 25 feet 4 inches

Answer 2

The height of the flagpole is
`25\ ft\ 4\ in`

Explanation:

we know that

If two figures are similar, the the ratio of its corresponding sides is proportional

Remember that

`1\ ft=12\ inches`

Convert the measures in inches

`3\ ft=3(12)=36\ in`

`5\ ft\ 4\ in=5(12)+4=64\ in`

`14\ ft\ 3\ in=14(12)+3=171\ in`

`(h)/(64)=(171)/(36)\\ \\h=171*64/36\\ \\h=304\ in`

Convert inches into (feet + inches)

`h=304\ in=304/12=25.33\ ft=25\ ft\ 4\ in`