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 23 feet 23 feet 374 feet 374 feet 17 feet 17 feet 23 inches

Answer 1

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

First, let's convert Myk's height into inches:
Myk's height = 5 feet 2 inches = 5 * 12 + 2 = 60 + 2 = 62 inches.

Given:
- Myk's height = 62 inches
- Myk's shadow = 84 inches
- Flagpole's shadow = 31 feet = 31 * 12 = 372 inches (since 1 foot = 12 inches)

Now we can set up the proportion based on similar triangles:

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

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

The equation becomes:

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

Now we can solve for \( h \):

1. Cross-multiply:

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

2. Calculate \( 62 \times 372 \):

\[
62 \times 372 = 23064
\]

3. Thus, we have:

\[
23064 = 84h
\]

4. Now, divide both sides by 84:

\[
h = \frac{23064}{84} \approx 274.43 \text{ inches}
\]

5. Convert inches to feet:

\[
h \text{ in feet} = \frac{274.43}{12} \approx 22.87 \text{ feet}
\]

Rounding to the nearest foot, the height of the flagpole is approximately **23 feet**.

Thus, the answer is **23 feet**.