To find the height of the flagpole using similar triangles, we can set up a proportion based on Myk's height and shadow length compared to the flagpole's height and shadow length.
First, we need to convert Myk's height to inches. Myk's height is 5 feet and 2 inches.
1 foot is 12 inches, so: \[ 5 \text{ feet} = 5 \times 12 = 60 \text{ inches} \] Adding the remaining 2 inches: \[ \text{Myk's height} = 60 + 2 = 62 \text{ inches} \]
Now, we can set up our proportion. Let \( h \) be the height of the flagpole in inches. We know:
- Myk's height: 62 inches
- Myk's shadow: 84 inches
- Flagpole shadow: 31 feet (which is \( 31 \times 12 = 372 \text{ inches} \))
Now, we can set up the proportion: \[ \frac{\text{Myk's height}}{\text{Myk's shadow}} = \frac{\text{Flagpole height}}{\text{Flagpole shadow}} \] Which translates to: \[ \frac{62}{84} = \frac{h}{372} \]
Now, we can cross-multiply to solve for \( h \): \[ 62 \times 372 = 84 \times h \] Calculating \( 62 \times 372 \): \[ 62 \times 372 = 23064 \] Now substituting back: \[ 23064 = 84h \] To solve for \( h \), divide both sides by 84: \[ h = \frac{23064}{84} \approx 274 \]
Now converting \( h \) from inches to feet (since 1 foot = 12 inches): \[ \frac{274}{12} \approx 22.83 \text{ feet} \]
Rounding to the nearest foot gives us approximately 23 feet.
Thus, the height of the flagpole is: B. 23 feet.
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