Question

Myk is 5 feet and 2 inches tall, and their shadow is 84 inches tall. The flagpole next to them has a shadow that is 31 feet long. Myk uses similar triangles to find the height of the flagpole. Can you calculate the height of the flagpole to the nearest foot?(1 point)
Responses

374 feet
374 feet

23 inches
23 inches

17 feet
17 feet

23 feet

Answer 1

To find the height of the flagpole using similar triangles, we can set up a proportion based on the heights and the lengths of the shadows.

First, let's convert Myk's height into inches for consistency:
- Myk's height: 5 feet 2 inches = (5 × 12) + 2 = 60 + 2 = 62 inches.

Now we have:
- Myk's height = 62 inches
- Myk's shadow = 84 inches
- Flagpole's shadow = 31 feet = 31 × 12 = 372 inches

Let \( h \) be the height of the flagpole in inches.

Using the property of similar triangles, we have:

\[
\frac{\text{Height of Myk}}{\text{Shadow of Myk}} = \frac{\text{Height of Flagpole}}{\text{Shadow of Flagpole}}
\]

This gives us the equation:

\[
\frac{62}{84} = \frac{h}{372}
\]

Now we can cross-multiply:

\[
62 \times 372 = 84 \times h
\]

Calculate \( 62 \times 372 \):

\[
62 \times 372 = 23064
\]

So we have:

\[
23064 = 84h
\]

Now, solve for \( h \):

\[
h = \frac{23064}{84} \approx 274.0 \text{ inches}
\]

To convert inches to feet, we divide by 12:

\[
\frac{274.0}{12} \approx 22.83 \text{ feet}
\]

Rounding to the nearest foot gives us approximately 23 feet.

Thus, the height of the flagpole is **23 feet**.