To calculate the height of the flagpole using similar triangles, we can set up a proportion based on the corresponding heights and shadows.
-
Convert Myk's height into inches:
Myk's height = 5 feet 2 inches = (5 × 12) + 2 = 60 + 2 = 62 inches. -
Set up the proportion using the heights and shadows:
Let \( h \) be the height of the flagpole in inches.
The ratio of Myk's height to their shadow should be equal to the ratio of the flagpole's height to its shadow.This gives us the proportion:
\[ \frac{\text{Myk's height}}{\text{Myk's shadow}} = \frac{\text{Flagpole's height}}{\text{Flagpole's shadow}} \] Substituting the known values:
\[ \frac{62 \text{ inches}}{84 \text{ inches}} = \frac{h}{31 \text{ feet}} \]We need to convert 31 feet into inches:
\( 31 \text{ feet} = 31 \times 12 = 372 \text{ inches} \). -
Now the proportion looks like this:
\[ \frac{62}{84} = \frac{h}{372} \] -
Cross-multiply to solve for \( h \):
\[ 62 \times 372 = 84 \times h \]
\[ 23064 = 84h \]
\[ h = \frac{23064}{84} \approx 274 \] -
Convert the height of the flagpole from inches back to feet:
\( 274 \text{ inches} = \frac{274}{12} \approx 22.83 \text{ feet} \). -
Rounding to the nearest foot gives us:
Height of the flagpole = 23 feet.
Therefore, the height of the flagpole is 23 feet.
1 answer