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 32 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?

Answer 1

To find the height of the flagpole using the proportions of similar triangles, we can set up a ratio based on the information given.

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

• Myk’s height = 5 feet × 12 inches/foot + 2 inches = 60 inches + 2 inches = 62 inches.

Next, let’s denote:

• Myk’s height = 62 inches
• Myk’s shadow = 84 inches
• Flagpole height = unknown (let’s denote it as \( h \))
• Flagpole shadow = 32 feet = 32 × 12 inches = 384 inches

Using the property of similar triangles, we can set up the following proportion:

\[ \frac{\text{Height of Myk}}{\text{Length of Myk's shadow}} = \frac{\text{Height of flagpole}}{\text{Length of flagpole's shadow}} \]

Plugging in the values we have:

\[ \frac{62 \text{ inches}}{84 \text{ inches}} = \frac{h}{384 \text{ inches}} \]

Now, cross-multiply to solve for \( h \):

\[ 62 \times 384 = 84 \times h \]

Calculating \( 62 \times 384 \):

\[ 62 \times 384 = 23808 \]

Now, we have:

\[ 23808 = 84h \]

To find \( h \), divide both sides by 84:

\[ h = \frac{23808}{84} \approx 283.43 \text{ inches} \]

Now, convert this height from inches to feet:

\[ h \text{ in feet} = \frac{283.43 \text{ inches}}{12 \text{ inches/foot}} \approx 23.62 \text{ feet} \]

Rounding to the nearest foot:

\[ h \approx 24 \text{ feet} \]

Thus, the height of the flagpole is approximately 24 feet.