Question

cell towers a cell phone tower casts a shadow that is 100 feet long. at the same time, lia stands near the tower and casts a shadow that is 3 feet 4 inches long. if lia is 4 feet 6 inches tall, how tall is the cell phone tower?
need help?
ft

Explanation:

Step1: Convert units

Convert Lia's height and shadow length to inches.
Lia's height: \(4\) feet \(6\) inches \(=4\times12 + 6=54\) inches.
Lia's shadow: \(3\) feet \(4\) inches \(=3\times12+4 = 40\) inches.
Tower's shadow: \(100\) feet \(=100\times12 = 1200\) inches.

Step2: Set up proportion

Let the tower's height be \(h\) inches. Using the proportion \(\frac{\text{height}}{\text{shadow}}=\frac{\text{height}}{\text{shadow}}\), we have \(\frac{54}{40}=\frac{h}{1200}\).
Cross - multiply: \(40h=54\times1200\).

Step3: Solve for \(h\)

\(h=\frac{54\times1200}{40}\).
\(h = 54\times30=1620\) inches.
Convert back to feet: \(1620\div12 = 135\) feet.

Answer:

\(135\)