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)

Responses

374 feet
374 feet

23 feet
23 feet

23 inches
23 inches

17 feet
17 feet

1 answer

To find the height of the flagpole using similar triangles, we can set up a proportion using Myk’s height and shadow compared to the flagpole’s height and shadow.

  1. First, convert Myk's height from feet and inches to inches:

    • Myk's height = 5 feet 2 inches = (5 × 12) + 2 = 60 + 2 = 62 inches.
  2. Let \( h \) be the height of the flagpole in inches.

  3. The shadows are:

    • Myk's shadow = 84 inches
    • Flagpole's shadow = 31 feet = 31 × 12 = 372 inches.
  4. Set up the proportion using similar triangles: \[ \frac{\text{Myk's height}}{\text{Myk's shadow}} = \frac{\text{Flagpole's height}}{\text{Flagpole's shadow}} \] \[ \frac{62}{84} = \frac{h}{372} \]

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

  6. Convert \( h \) back to feet: \[ \text{Height in feet} = \frac{274}{12} \approx 22.83 \text{ feet} \approx 23 \text{ feet (to the nearest foot)} \]

Thus, the height of the flagpole is approximately 23 feet.