To find the height of the flagpole using similar triangles, we can set up a proportion based on the heights and the lengths of the shadows.
First, let's convert Myk's height into inches for consistency:
- Myk's height: 5 feet 2 inches = (5 × 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 × 12 = 372 inches
Let \( h \) be the height of the flagpole in inches.
Using the property of similar triangles, we have:
\[ \frac{\text{Height of Myk}}{\text{Shadow of Myk}} = \frac{\text{Height of Flagpole}}{\text{Shadow of Flagpole}} \]
This gives us the equation:
\[ \frac{62}{84} = \frac{h}{372} \]
Now we can cross-multiply:
\[ 62 \times 372 = 84 \times h \]
Calculate \( 62 \times 372 \):
\[ 62 \times 372 = 23064 \]
So we have:
\[ 23064 = 84h \]
Now, solve for \( h \):
\[ h = \frac{23064}{84} \approx 274.0 \text{ inches} \]
To convert inches to feet, we divide by 12:
\[ \frac{274.0}{12} \approx 22.83 \text{ feet} \]
Rounding to the nearest foot gives us approximately 23 feet.
Thus, the height of the flagpole is 23 feet.
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