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?

ft

Explanation:

Step1: Convert lengths to inches

1 foot = 12 inches. Lia's height is $4\times12 + 6=54$ inches. Lia's shadow is $3\times12+4 = 40$ inches. Tower's shadow is $100\times12 = 1200$ inches.

Step2: Set up proportion

Let the height of the tower be $h$ inches. Since the ratios of object - height to shadow - length are equal, we have $\frac{h}{1200}=\frac{54}{40}$.

Step3: Solve for $h$

Cross - multiply: $40h=54\times1200$. Then $h=\frac{54\times1200}{40}=1620$ inches.

Step4: Convert back to feet

Since 1 foot = 12 inches, the height of the tower in feet is $\frac{1620}{12}=135$ feet.

Answer:

135