Question

A 10​-ft vertical post casts a 12​-in shadow at the same time a nearby cell phone tower casts a 126​-ft shadow. How tall is the cell phone​ tower?

Answer 1

The cell phone tower is 1260 feet tall

Solution:

Given that 10​-ft vertical post casts a 12​-in shadow

At the same time a nearby cell phone tower casts a 126​-ft shadow

To find: height of cellphone tower

We can use proportion to solve the sum

$\frac{\text {height of post }}{\text {shadow of post}}=\frac{\text {height of tower}}{\text {shadow of tower}}$

Here,

Let "x" be the height of tower

height of post = 10 feet

shadow of tower = 126 feet

shadow of post = 12 inches

We know that,

1 inches = 0.0833333 foot

12 inches = 12 x 0.0833333 foot = 1 foot

shadow of post = 1 foot

Thus the proportion becomes,

$\frac{10}{1} = \frac{x}{126}$

$10 \times 126 = x \times 1\\\\x = 10 \times 126 = 1260$

Thus the cell phone tower is 1260 feet tall