Question

A 66​-ft vertical post casts a 1010​-in shadow at the same time a nearby cell phone tower casts a 125125​-ft shadow. How tall is the cell phone​ tower?
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Part 1
The cell phone​ tower's height is enter your response here ft.

Answer 1

To find the height of the cell phone tower, we can set up a proportion based on the similar triangles formed by the vertical post and its shadow and the cell phone tower and its shadow.

Let \( h \) be the height of the cell phone tower.

We can set up the following proportion:

\[
\frac{\text{Height of the post}}{\text{Length of the post's shadow}} = \frac{\text{Height of the tower}}{\text{Length of the tower's shadow}}
\]

Plugging in the known values:

\[
\frac{66\, \text{ft}}{1010\, \text{in}} = \frac{h}{125\, \text{ft}}
\]

First, we need to convert the shadow of the post from inches to feet because the height of the post is given in feet. There are 12 inches in a foot, so:

\[
1010\, \text{in} = \frac{1010}{12}\, \text{ft} \approx 84.1667\, \text{ft}
\]

Now we can rewrite our proportion:

\[
\frac{66}{84.1667} = \frac{h}{125}
\]

Now we cross-multiply:

\[
66 \times 125 = h \times 84.1667
\]

Calculating \( 66 \times 125 \):

\[
8250 = h \times 84.1667
\]

Now, solve for \( h \):

\[
h = \frac{8250}{84.1667} \approx 98.1\, \text{ft}
\]

Therefore, the height of the cell phone tower is approximately:

\[
\text{The cell phone tower's height is } 98.1\, \text{ft.}
\]