Final answer:
Using proportions based on similar triangles, the height of the flagpole is found to be 30 feet, which doesn't match any of the provided options, indicating a possible error in the question.
Step-by-step explanation:
To solve the problem involving the flagpole and the person's shadow to find the height of the flagpole, we can use proportions based on similar triangles formed by the objects and their shadows. Similar triangles have corresponding sides that are in proportion. The problem states that a 6-foot-tall person casts a shadow 1.75 feet long, and at the same time, the flagpole casts a shadow 8.75 feet long. To find the height of the flagpole, we set up a proportion:
Person's height / Person's shadow length = Flagpole's height / Flagpole's shadow length
6 ft / 1.75 ft = Flagpole's height / 8.75 ft
Cross-multiplying gives us:
6 ft × 8.75 ft = Flagpole's height × 1.75 ft
We then divide both sides by 1.75 ft to isolate the flagpole's height:
Flagpole's height = (6 ft × 8.75 ft) / 1.75 ft
Flagpole's height = 52.5 ft² / 1.75 ft
Flagpole's height = 30 ft
So the correct answer is that the flagpole is 30 feet tall, which is not one of the provided options (a) 4 feet, (b) 10 feet, (c) 14 feet, (d) 18 feet. Therefore, there appears to be a mistake in the question options or the problem itself.