Question

A person who is 72 inches tall casts a shadow that is 48 inches long. If a nearby flag pole casts a shadow that is 32 feet long at the same time, then how tall is the flag pole to the nearest foot

Answer 1

The answer is 48 feet.

Let's convert the units to inches for consistency:
1 foot = 12 inches

The person's height of 72 inches corresponds to a shadow length of 48 inches. Similarly, the flagpole's shadow length of 32 feet corresponds to its unknown height in inches.

We can set up the proportion:
Person's height / Person's shadow length = Flagpole's height / Flagpole's shadow length

Plugging in the values:
72 inches / 48 inches = Flagpole's height / (32 feet * 12 inches/foot)

Simplifying:
72/48 = Flagpole's height / (32 * 12)
3/2 = Flagpole's height / 384

To find the flagpole's height, we can cross-multiply:
(3/2) * 384 = Flagpole's height

Flagpole's height ≈ 576 inches

Since the question asks for the height of the flagpole to the nearest foot, we convert 576 inches to feet:
576 inches / 12 inches/foot ≈ 48 feet

Therefore, the flagpole's height is approximately 48 feet.