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.