Question

a cell phone tower casts a 100 - foot shadow. at the same time, a 4 - foot - 6 - inch post near the tower casts a shadow of 3 feet 4 inches. how tall is the cell phone tower?

Explanation:

Step1: Convert lengths to inches

1 foot = 12 inches. The post is 4 - foot - 6 - inch, so its height in inches is $4\times12 + 6=54$ inches. The post's shadow is 3 feet 4 inches, so its length in inches is $3\times12+4 = 40$ inches. The tower's shadow is 100 feet, so its length in inches is $100\times12=1200$ inches.

Step2: Set up proportion

Let the height of the tower be $h$ inches. Since the ratio of the object's height to its shadow length is the same for both the post and the tower, we have the proportion $\frac{54}{40}=\frac{h}{1200}$.

Step3: Solve for $h$

Cross - multiply: $40h=54\times1200$. Then $h=\frac{54\times1200}{40}=54\times30 = 1620$ 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