To find the height of the flagpole using similar triangles, we'll set up a proportion based on the heights and shadows.
First, let's convert Myk's height into inches:
- Myk's height: 5 feet 2 inches = \( 5 \times 12 + 2 = 60 + 2 = 62 \) inches.
Now we have:
- Myk's height = 62 inches
- Myk's shadow = 84 inches
- Flagpole's shadow = 31 feet = \( 31 \times 12 = 372 \) inches
We can set up a proportion using the heights and their respective shadows:
\[ \frac{\text{Myk's height}}{\text{Myk's shadow}} = \frac{\text{Flagpole's height}}{\text{Flagpole's shadow}} \]
Let \( h \) be the height of the flagpole in inches. Therefore, we have:
\[ \frac{62}{84} = \frac{h}{372} \]
Now we can cross-multiply to solve for \( h \):
\[ 62 \times 372 = 84 \times h \]
Calculating \( 62 \times 372 \):
\[ 62 \times 372 = 23064 \]
So we have:
\[ 23064 = 84h \]
Now, divide both sides by 84 to isolate \( h \):
\[ h = \frac{23064}{84} \approx 274.0 \text{ inches} \]
Now, to convert the height from inches to feet:
\[ \text{Height in feet} = \frac{274.0}{12} \approx 22.83 \text{ feet} \]
Rounding to the nearest foot gives us \( 23 \) feet.
The correct answer is \( \boxed{23} \) feet.
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