To find the height of the flagpole using similar triangles, we first need to convert Myk's height into inches since all measurements need to be in the same unit. Myk is 5 feet 2 inches tall:
\[ 5 \text{ feet} = 5 \times 12 = 60 \text{ inches} \] \[ \text{total height of Myk} = 60 \text{ inches} + 2 \text{ inches} = 62 \text{ inches} \]
Now we have the following information:
- Height of Myk = 62 inches
- 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 can set up a proportion:
\[ \frac{\text{Height of Myk}}{\text{Shadow of Myk}} = \frac{\text{Height of Flagpole}}{\text{Shadow of Flagpole}} \]
Let \( h \) be the height of the flagpole. The proportion becomes:
\[ \frac{62}{84} = \frac{h}{372} \]
Now, cross-multiply to solve for \( h \):
\[ 62 \times 372 = 84 \times h \] \[ 23064 = 84h \] \[ h = \frac{23064}{84} \approx 274 \]
Now, we'll convert \( h \) to feet:
\[ \text{Height of the flagpole in feet} = \frac{274}{12} \approx 22.83 \text{ feet} \]
Rounding to the nearest foot gives us:
23 feet.
Therefore, the height of the flagpole is 23 feet.
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