A 5-foot tall woman has a shadow of 3 feet. If the flagpole's shadow is 21 feet, how tall is the flagpole?

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Multiple Choice

A 5-foot tall woman has a shadow of 3 feet. If the flagpole's shadow is 21 feet, how tall is the flagpole?

Explanation:
The main idea is that heights and their shadows form proportional relationships when the sun is at a fixed angle. The same sun angle gives a constant height-to-shadow ratio for any object. For the woman, the height-to-shadow ratio is 5 feet to 3 feet. The flagpole, with a 21-foot shadow, must have a height that preserves that same ratio. Set up the proportion: 5/3 = height/21. Solve for height: height = 21 × (5/3) = 35 feet. So the flagpole is 35 feet tall. The other numbers wouldn’t maintain the same height-to-shadow ratio under the same sun angle, so they don’t fit.

The main idea is that heights and their shadows form proportional relationships when the sun is at a fixed angle. The same sun angle gives a constant height-to-shadow ratio for any object.

For the woman, the height-to-shadow ratio is 5 feet to 3 feet. The flagpole, with a 21-foot shadow, must have a height that preserves that same ratio. Set up the proportion: 5/3 = height/21. Solve for height: height = 21 × (5/3) = 35 feet.

So the flagpole is 35 feet tall. The other numbers wouldn’t maintain the same height-to-shadow ratio under the same sun angle, so they don’t fit.

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