Question

a 4-ft vertical post casts a 20-in shadow at the same time a nearby cell phone tower casts a 115-ft shadow. how tall is the cell phone tower? (simplify your answer.) the cell phone tower’s height is \\(\square\\) ft.

Explanation:

Step1: Convert units to be consistent

First, convert the shadow length of the post from inches to feet. Since 1 foot = 12 inches, 20 inches = $\frac{20}{12}$ = $\frac{5}{3}$ feet.

Step2: Set up proportion

Let \( h \) be the height of the cell phone tower. The ratio of height to shadow length should be the same for both the post and the tower. So we have the proportion: $\frac{4}{\frac{5}{3}}=\frac{h}{115}$

Step3: Solve for \( h \)

Cross - multiply: $\frac{5}{3}h = 4\times115$
$\frac{5}{3}h = 460$
Multiply both sides by $\frac{3}{5}$: $h = 460\times\frac{3}{5}$
$h = 276$

Answer:

276