Question

Proving Similar Triangles Quick Check 5 of 55 of 5 Items Question 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 inches 23 inches 17 feet 17 feet 23 feet 23 feet Skip to navigation page 23 of 23 Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.

Answer 1

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

1. Convert Myk's height to inches: Myk's height = 5 feet 2 inches = $5\times 12+2=62$ inches.

2. Myk's shadow length = 84 inches.

3. Flagpole shadow length = 31 feet = $31\times 12=372$ inches.

Now, we can set up the proportion using the heights and shadow lengths:

$$\frac{\text{Height of Myk}}{\text{Shadow of Myk}}=\frac{\text{Height of Flagpole}}{\text{Shadow of Flagpole}}$$

Let $h$ be the height of the flagpole in inches. Then the proportion is:

$$\frac{62}{84}=\frac{h}{372}$$

Now, we can cross-multiply to solve for $h$:

$$62\cdot 372=84\cdot h$$

Calculating the left-hand side:

$$62\cdot 372=23064$$

So we have:

$$23064=84h$$

Now, divide both sides by 84:

$$h=\frac{23064}{84}\approx 274$$

Since we need to convert inches back to feet, we divide by 12:

$$\frac{274}{12}\approx 22.83\text{ feet}$$

Rounding to the nearest foot, the height of the flagpole is approximately 23 feet.

So, the correct answer is 23 feet.