Question

a 10-ft vertical post casts a 14-in shadow at the same time a nearby cell phone tower casts a 119-ft shadow. how tall is the cell phone tower?
the cell phone towers height is \\(\square\\) ft.
(simplify your answer.)

Explanation:

Step1: Convert units to be consistent

Convert 14 inches to feet: $14\ \text{in} = \frac{14}{12}\ \text{ft} = \frac{7}{6}\ \text{ft}$

Step2: Set up proportion

Let $h$ = tower height. Equate height-shadow ratios:
$\frac{10}{\frac{7}{6}} = \frac{h}{119}$

Step3: Solve for $h$

Rearrange to isolate $h$:
$h = 10 \times \frac{6}{7} \times 119$
Calculate: $10 \times 6 \times 17 = 1020$

Answer:

1020