To find the height of the flagpole using similar triangles, we can set up a proportion based on the heights and lengths of the shadows.
-
Convert Myk's height to inches: Myk is 5 feet and 2 inches tall. \[ \text{Myk's height in inches} = 5 \times 12 + 2 = 60 + 2 = 62 \text{ inches} \]
-
Myk's shadow: \[ \text{Myk's shadow length} = 84 \text{ inches} \]
-
Flagpole's shadow: \[ \text{Flagpole's shadow length} = 31 \text{ feet} \] Convert the flagpole's shadow length to inches: \[ 31 \text{ feet} \times 12 \text{ inches/foot} = 372 \text{ inches} \]
-
Set up the proportion using similar triangles: Let \( h \) be the height of the flagpole in inches.
The ratio of Myk's height to Myk's shadow is equal to the ratio of the flagpole's height to the flagpole's shadow: \[ \frac{62 \text{ inches}}{84 \text{ inches}} = \frac{h}{372 \text{ inches}} \]
-
Cross-multiply to solve for \( h \): \[ 62 \times 372 = 84 \times h \] \[ 23064 = 84h \] \[ h = \frac{23064}{84} \approx 274.43 \text{ inches} \]
-
Convert the height of the flagpole back to feet: \[ h \text{ in feet} = \frac{274.43 \text{ inches}}{12} \approx 22.87 \text{ feet} \]
-
Round to the nearest foot: The height of the flagpole is approximately 23 feet.
Thus, the height of the flagpole is 23 feet.
1 answer