Question

a 10 - ft vertical post casts a 20 - in shadow at the same time a nearby cell phone tower casts a 125 - ft shadow. how tall is the cell phone tower? the cell phone tower’s height is 854 ft. (simplify your answer.)

Explanation:

Step1: Convert units

Since 1 foot = 12 inches, 20 inches = $\frac{20}{12}=\frac{5}{3}$ feet.

Step2: Set up proportion

Let the height of the cell - phone tower be $h$ feet. The ratio of the height of the post to its shadow is equal to the ratio of the height of the tower to its shadow. So we have the proportion $\frac{10}{\frac{5}{3}}=\frac{h}{125}$.

Step3: Cross - multiply and solve for $h$

Cross - multiplying gives $10\times125=\frac{5}{3}h$. Then $1250 = \frac{5}{3}h$. Multiply both sides by $\frac{3}{5}$ to isolate $h$. So $h=\frac{1250\times3}{5}=750$ feet.

Answer:

750 ft