To find the height of the flagpole using the concept of similar triangles, we can set up a proportion based on the heights and lengths of the shadows.
First, let's convert Myk's height to inches:
- Myk's height = 5 feet 2 inches = (5 * 12) + 2 = 60 + 2 = 62 inches.
Now we can set up the proportion. Let \( h \) be the height of the flagpole in inches.
The corresponding lengths of the shadows are:
- Myk's shadow = 84 inches,
- Flagpole's shadow = 31 feet = 31 * 12 = 372 inches.
Using similar triangles, we set up the following proportion:
\[ \frac{\text{Myk's height}}{\text{Myk's shadow}} = \frac{\text{Flagpole's height}}{\text{Flagpole's shadow}} \]
Substituting in the known values:
\[ \frac{62}{84} = \frac{h}{372} \]
Now, we can cross-multiply to solve for \( h \):
\[ 62 \times 372 = 84 \times h \]
Calculating \( 62 \times 372 \):
\[ 62 \times 372 = 23064 \]
So, we have:
\[ 23064 = 84h \]
Now divide both sides by 84 to solve for \( h \):
\[ h = \frac{23064}{84} \approx 274.43 \text{ inches} \]
To convert inches to feet:
\[ h \text{ in feet} = \frac{274.43}{12} \approx 22.87 \text{ feet} \]
Rounding this to the nearest foot, we get approximately:
\[ \text{Height of the flagpole} \approx 23 \text{ feet} \]
Therefore, the height of the flagpole is 23 feet.