To find the height of the flagpole using similar triangles, we can set up a proportion based on the known height and shadow lengths.
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Convert Myk's height to inches: Myk's height = 5 feet 2 inches = \(5 \times 12 + 2 = 62\) inches.
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Myk's shadow length = 84 inches.
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Flagpole shadow length = 31 feet = \(31 \times 12 = 372\) inches.
Now, we can set up the proportion using the heights and shadow lengths:
\[ \frac{\text{Height of Myk}}{\text{Shadow of Myk}} = \frac{\text{Height of Flagpole}}{\text{Shadow of Flagpole}} \]
Let \(h\) be the height of the flagpole in inches. Then the proportion is:
\[ \frac{62}{84} = \frac{h}{372} \]
Now, we can cross-multiply to solve for \(h\):
\[ 62 \cdot 372 = 84 \cdot h \]
Calculating the left-hand side:
\[ 62 \cdot 372 = 23064 \]
So we have:
\[ 23064 = 84h \]
Now, divide both sides by 84:
\[ h = \frac{23064}{84} \approx 274 \]
Since we need to convert inches back to feet, we divide by 12:
\[ \frac{274}{12} \approx 22.83 \text{ feet} \]
Rounding to the nearest foot, the height of the flagpole is approximately 23 feet.
So, the correct answer is 23 feet.
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