Myk is 5 feet and 2 inches tall, and their shadow is 84 inches tall. The flagpole next to them has a shadow that is 31 feet long. Myk uses similar triangles to find the height of the flagpole. Can you calculate the height of the flagpole to the nearest foot?(1 point)

Question

Responses

23 feet
23 feet

23 inches
23 inches

374 feet
374 feet

17 feet

Answer 1

To find the height of the flagpole using similar triangles, we can set up a proportion based on the heights and shadow lengths.

1. Convert Myk's height to inches:

   • Myk is 5 feet and 2 inches tall.
   • 5 feet = 5 × 12 = 60 inches.
   • So, Myk's height = 60 inches + 2 inches = 62 inches.

2. Set up the proportion: \[ \frac{\text{Myk's height}}{\text{Myk's shadow}} = \frac{\text{Flagpole's height}}{\text{Flagpole's shadow}} \]

   We know:

   • Myk's height = 62 inches
   • Myk's shadow = 84 inches
   • Flagpole's shadow = 31 feet = 31 × 12 = 372 inches

   Let \( h \) be the height of the flagpole in inches. Then the proportion is: \[ \frac{62}{84} = \frac{h}{372} \]

3. Cross-multiply and solve for \( h \): \[ 62 \times 372 = 84 \times h \] \[ 23064 = 84h \] \[ h = \frac{23064}{84} = 274 \]

4. Convert the height of the flagpole to feet:

   • Since 1 foot = 12 inches, we convert by dividing by 12: \[ \text{Height in feet} = \frac{274}{12} \approx 22.83 \]

5. Round to the nearest foot:

   • Rounding 22.83 gives us 23 feet.

Thus, the height of the flagpole is 23 feet.