Question

a flagpole casts a shadow that is 16 feet long. at the same time, a person standing nearby who is 5 feet 6 inch casts a shadow that is 44 inches long. how tall is the flagpole? flagpole: \boxed{} feet

Explanation:

Step1: Convert units to inches

The person's height is 5 feet 6 inches. Since 1 foot = 12 inches, 5 feet = \(5\times12 = 60\) inches, so total height is \(60 + 6=66\) inches. The flagpole's shadow is 16 feet, which is \(16\times12 = 192\) inches. The person's shadow is 44 inches.

Step2: Set up proportion

Let \(h\) be the flagpole's height in inches. The proportion of height to shadow length should be equal: \(\frac{66}{44}=\frac{h}{192}\).

Step3: Solve for \(h\)

Cross - multiply: \(44h=66\times192\). Then \(h=\frac{66\times192}{44}\). Simplify: \(\frac{66}{44}=\frac{3}{2}\), so \(h=\frac{3\times192}{2}=3\times96 = 288\) inches.

Step4: Convert back to feet

Since 1 foot = 12 inches, \(288\div12 = 24\) feet.

Answer:

24