To solve for the height of the flagpole using similar triangles, we first need to convert all measurements to the same unit.
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Myk's height:
- Myk is 5 feet and 2 inches tall.
- There are 12 inches in a foot, so: \[ 5 \text{ feet} = 5 \times 12 = 60 \text{ inches} \] Adding the 2 inches gives: \[ 60 \text{ inches} + 2 \text{ inches} = 62 \text{ inches} \]
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The shadow of Myk is given as 84 inches long.
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The shadow of the flagpole is given as 31 feet long. We convert this to inches: \[ 31 \text{ feet} = 31 \times 12 = 372 \text{ inches} \]
Now we can set up a proportion using similar triangles: Let \( h \) be the height of the flagpole in inches. The proportion is:
\[ \frac{\text{Height of Myk}}{\text{Shadow of Myk}} = \frac{\text{Height of Flagpole}}{\text{Shadow of Flagpole}} \]
Substituting the known values: \[ \frac{62}{84} = \frac{h}{372} \]
Cross-multiply to solve for \( h \): \[ 62 \times 372 = 84 \times h \] Calculating \( 62 \times 372 \): \[ 62 \times 372 = 23064 \] This gives us: \[ 23064 = 84h \] Now divide both sides by 84 to isolate \( h \): \[ h = \frac{23064}{84} \approx 274.5 \text{ inches} \]
We can convert this height to feet by dividing by 12: \[ \frac{274.5}{12} \approx 22.875 \text{ feet} \]
Rounding this to the nearest foot gives us: \[ \approx 23 \text{ feet} \]
Therefore, the height of the flagpole is 23 feet.
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