To find the height of the flagpole using similar triangles, we can set up a proportion using Myk’s height and shadow compared to the flagpole’s height and shadow.
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First, convert Myk's height from feet and inches to inches:
- Myk's height = 5 feet 2 inches = (5 × 12) + 2 = 60 + 2 = 62 inches.
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Let \( h \) be the height of the flagpole in inches.
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The shadows are:
- Myk's shadow = 84 inches
- Flagpole's shadow = 31 feet = 31 × 12 = 372 inches.
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Set up the proportion using similar triangles: \[ \frac{\text{Myk's height}}{\text{Myk's shadow}} = \frac{\text{Flagpole's height}}{\text{Flagpole's shadow}} \] \[ \frac{62}{84} = \frac{h}{372} \]
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Cross-multiply to solve for \( h \): \[ 62 \times 372 = 84 \times h \] \[ 23064 = 84h \] \[ h = \frac{23064}{84} \] \[ h = 274 \]
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Convert \( h \) back to feet: \[ \text{Height in feet} = \frac{274}{12} \approx 22.83 \text{ feet} \approx 23 \text{ feet (to the nearest foot)} \]
Thus, the height of the flagpole is approximately 23 feet.
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