To find the height of the flagpole using similar triangles, we can set up a proportion based on the heights and shadows of Myk and the flagpole.
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Convert Myk’s height to inches:
- Myk is 5 feet 2 inches tall.
- Convert 5 feet to inches: \(5 \times 12 = 60\) inches.
- Total height of Myk in inches: \(60 + 2 = 62\) inches.
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Identify the lengths of shadows:
- Myk's shadow length: 84 inches.
- Flagpole's shadow length: 31 feet, which we convert to inches: \(31 \times 12 = 372\) inches.
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Set up the proportion: \[ \frac{\text{Height of Myk}}{\text{Shadow of Myk}} = \frac{\text{Height of Flagpole}}{\text{Shadow of Flagpole}} \] \[ \frac{62}{84} = \frac{h}{372} \]
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Cross-multiply to solve for \(h\) (the height of the flagpole): \[ 62 \times 372 = 84 \times h \] \[ 23064 = 84h \] \[ h = \frac{23064}{84} \] \[ h \approx 274.57 \text{ inches} \]
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Convert the height from inches to feet: \[ \frac{274.57}{12} \approx 22.88 \text{ feet} \]
Rounding to the nearest foot, the height of the flagpole is approximately 23 feet.
Thus, the correct answer is: b. 23 feet.
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