Dru is challanged by her geomtry 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 own shadow. If Dru is 5ft 6inches 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?
The sides of similar triangles are in the same ratio
so wouldn't the flag pole be 14 times as tall as she is?
why do elephants have pointy tails
to make them more streamlined
To estimate the height of the flagpole, Dru can use the concept of similar triangles. The ratio of corresponding sides of similar triangles is equal, so she can use her own height and shadow length as a ratio to determine the flagpole's height.
Given that Dru is 5 feet 6 inches tall and her shadow is 14 times as long as her own height, we can calculate her shadow length:
Dru's height = 5 ft 6 in = 5.5 ft (Converting inches to feet, 1 ft = 12 in)
Dru's shadow length = Dru's height * 14 = 5.5 ft * 14 = 77 ft
Now we can set up the proportion:
Dru's shadow length / Dru's height = Flagpole's shadow length / Flagpole's height
77 ft / 5.5 ft = Flagpole's shadow length / Flagpole's height
Flagpole's shadow length = 14 * Dru's shadow length = 14 * 77 ft = 1078 ft
So, the flagpole's shadow length is approximately 1078 ft.
Now we can solve for the flagpole's height:
Flagpole's shadow length / Flagpole's height = Dru's shadow length / Dru's height
1078 ft / Flagpole's height = 77 ft / 5.5 ft
Cross-multiplying:
1078 ft * 5.5 ft = 77 ft * Flagpole's height
5929 ft² = 77 ft * Flagpole's height
Dividing both sides by 77 ft:
5929 ft² / 77 ft = Flagpole's height
77 ft ≈ 76.97 ft
So, the approximate height of the flagpole is 76.97 ft.