Dru is challenged by her geometry teacher to estimate the height of the school flag pole without measuring. She decided to walk off the length of the shadow cast by the pole by successively walking the noted length of her shadow. If dry is 5ft 6 in.tall and she estimates the flagpole shadow is 14 times as long as her own shadow, then what is the approximate height of the flag pole?
If the pole's shadow is 14 times as long as her shadow, then the pole is 14 times as tall as she is.
14(5.5) = 77 feet
To estimate the height of the flagpole, Dru can use the proportion of her height to her shadow length and apply it to the flagpole's shadow length.
Given information:
- Dru's height: 5 ft 6 in
- Dru's shadow length: X (unknown)
- Flagpole's shadow length: 14 times Dru's shadow length
Let's convert Dru's height to a single unit of measurement (feet):
Dru's height = 5 ft + 6 in/12 ft (1 ft = 12 in)
= 5.5 ft
Now, we can set up a proportion to find Dru's shadow length:
Dru's height / Dru's shadow length = Flagpole's height / Flagpole's shadow length
Since we want to find the flagpole's height, let's rearrange the equation:
Flagpole's height = (Flagpole's shadow length / Dru's shadow length) * Dru's height
We are given that the flagpole's shadow length is 14 times Dru's shadow length:
Flagpole's shadow length = 14 * Dru's shadow length
Substituting this into the equation for the flagpole's height:
Flagpole's height = (14 * Dru's shadow length / Dru's shadow length) * Dru's height
Simplifying:
Flagpole's height = 14 * Dru's height
Now, we can calculate the approximate height of the flagpole:
Flagpole's height = 14 * 5.5 ft
= 77 ft
Therefore, the approximate height of the flagpole is 77 feet.