To determine the height of the flagpole using similar triangles, we start by converting Myk's height into inches. Myk is 5 feet 2 inches tall, which converts as follows:
\[ 5 \text{ feet} = 5 \times 12 = 60 \text{ inches} \] \[ \text{Height of Myk} = 60 + 2 = 62 \text{ inches} \]
Next, we know the length of Myk's shadow and the length of the flagpole's shadow:
- Length of Myk's shadow = 84 inches
- Length of the flagpole's shadow = 31 feet = \( 31 \times 12 = 372 \) inches
Using the properties of similar triangles, we set up the following proportion:
\[ \frac{\text{Height of Myk}}{\text{Length of Myk's shadow}} = \frac{\text{Height of Flagpole}}{\text{Length of Flagpole's shadow}} \]
Let \( h \) be the height of the flagpole. Then our equation becomes:
\[ \frac{62}{84} = \frac{h}{372} \]
To find \( h \), we can cross-multiply:
\[ 62 \times 372 = 84 \times h \]
Calculating \( 62 \times 372 \):
\[ 62 \times 372 = 23064 \]
So we have:
\[ 23064 = 84h \]
Now, divide both sides by 84 to solve for \( h \):
\[ h = \frac{23064}{84} \approx 274 \]
To the nearest foot, \( h \) equals 274 inches. To convert inches to feet, we divide by 12:
\[ \frac{274}{12} \approx 22.83 \]
Rounding to the nearest foot gives us 23 feet.
Thus, the height of the flagpole is 23 feet.
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