Question

7 Cassie wants to determine the length of the shadow that a 20-foot tall telephone pole casts without measuring it. If Cassie's mailbox, which is 45 inches in height, casts a shadow that is 22.5 inches in length, how long is the shadow that the telephone pole casts?

Answer 1

10 ft

Explanation:

In order to solve this question, we need to set up a proportion:

`\frac{\textrm{Height of mailbox}}{\textrm{Length of shadow}} = \frac{\textrm{Height of telephone pole}}{\textrm{Length of shadow}}`

Replacing with actual values:

`\frac{45 \textrm{ in}}{22.5 \textrm{ in}} = \frac{20 \textrm{ ft}}{x \textrm{ ft}}`

Cross-multiplying:

`45*{x} = 20*{22.5}\\45x = 450`

Dividing both sides by 45:

`(45x)/(45) = (450)/(45)\\\\x = 10`

Therefore, the length of the telephone pole's shadow is 10 ft.