Question

How tall is the flagpole if a 40-inch-tall boy casts a 6-foot shadow and the flagpole casts a 15-foot shadow?

Answer 1

To find the height of the flagpole based on the given information, we can use the principle of similar triangles. The ratio of the height of an object to the length of its shadow is the same for both the boy and the flagpole.

Given:
- The height of the boy = 40 inches
- The length of the boy's shadow = 6 feet
- The length of the flagpole's shadow = 15 feet

First, we need to convert the boy's height into feet since the shadow lengths are in feet.

\[
40 \text{ inches} = \frac{40}{12} \text{ feet} = \frac{10}{3} \text{ feet} \approx 3.33 \text{ feet}
\]

Now, we can set up the ratio of the heights to the shadows:

\[
\frac{\text{height of the boy}}{\text{length of the boy's shadow}} = \frac{\text{height of the flagpole}}{\text{length of the flagpole's shadow}}
\]

Substituting the known values:

\[
\frac{\frac{10}{3}}{6} = \frac{x}{15}
\]

Where \( x \) is the height of the flagpole.

Next, we cross-multiply to solve for \( x \):

\[
\frac{10}{3} \cdot 15 = x \cdot 6
\]

\[
50 = 6x
\]

To find \( x \), divide both sides by 6:

\[
x = \frac{50}{6} = \frac{25}{3} \approx 8.33 \text{ feet}
\]

Therefore, the height of the flagpole is approximately \( \frac{25}{3} \) feet or about 8.33 feet.