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 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?

a. 23 inches
b. 23 feet
c. 17 feet
d. 374 feet

Answer 1

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

1. **Convert Myk’s height to inches**:
- Myk is 5 feet 2 inches tall.
- Convert 5 feet to inches: \(5 \times 12 = 60\) inches.
- Total height of Myk in inches: \(60 + 2 = 62\) inches.

2. **Identify the lengths of shadows**:
- Myk's shadow length: 84 inches.
- Flagpole's shadow length: 31 feet, which we convert to inches: \(31 \times 12 = 372\) inches.

3. **Set up the proportion**:
\[
\frac{\text{Height of Myk}}{\text{Shadow of Myk}} = \frac{\text{Height of Flagpole}}{\text{Shadow of Flagpole}}
\]
\[
\frac{62}{84} = \frac{h}{372}
\]

4. **Cross-multiply to solve for \(h\)** (the height of the flagpole):
\[
62 \times 372 = 84 \times h
\]
\[
23064 = 84h
\]
\[
h = \frac{23064}{84}
\]
\[
h \approx 274.57 \text{ inches}
\]

5. **Convert the height from inches to feet**:
\[
\frac{274.57}{12} \approx 22.88 \text{ feet}
\]

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

Thus, the correct answer is:
**b. 23 feet**.