Duplicate Question
The question on this page has been marked as a duplicate question.
Original 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 lon...Asked by Drywall.
Myk is 5 feet and 2 inches tall, and their shadow is 84 inches ta;;. The flagpole next to them has a shadow that is 31 feet long. Myk uses similar triangles find the height of the flagpole. Can you calculate the height of the flagpole to the nearest foot?
A. 374 feet.
B. 23 feet.
C. 17 feet.
D. 23 feet.
A. 374 feet.
B. 23 feet.
C. 17 feet.
D. 23 feet.
Answers
Answered by
Drywall.
Thank you very much. :)
Answered by
GPT-4o mini
To find the height of the flagpole using similar triangles, we'll set up a proportion based on the heights and shadows.
First, let's convert Myk's height into inches:
- Myk's height: 5 feet 2 inches = \( 5 \times 12 + 2 = 60 + 2 = 62 \) inches.
Now we have:
- Myk's height = 62 inches
- Myk's shadow = 84 inches
- Flagpole's shadow = 31 feet = \( 31 \times 12 = 372 \) inches
We can set up a proportion using the heights and their respective shadows:
\[
\frac{\text{Myk's height}}{\text{Myk's shadow}} = \frac{\text{Flagpole's height}}{\text{Flagpole's shadow}}
\]
Let \( h \) be the height of the flagpole in inches. Therefore, we have:
\[
\frac{62}{84} = \frac{h}{372}
\]
Now we can cross-multiply to solve for \( h \):
\[
62 \times 372 = 84 \times h
\]
Calculating \( 62 \times 372 \):
\[
62 \times 372 = 23064
\]
So we have:
\[
23064 = 84h
\]
Now, divide both sides by 84 to isolate \( h \):
\[
h = \frac{23064}{84} \approx 274.0 \text{ inches}
\]
Now, to convert the height from inches to feet:
\[
\text{Height in feet} = \frac{274.0}{12} \approx 22.83 \text{ feet}
\]
Rounding to the nearest foot gives us \( 23 \) feet.
The correct answer is \( \boxed{23} \) feet.
First, let's convert Myk's height into inches:
- Myk's height: 5 feet 2 inches = \( 5 \times 12 + 2 = 60 + 2 = 62 \) inches.
Now we have:
- Myk's height = 62 inches
- Myk's shadow = 84 inches
- Flagpole's shadow = 31 feet = \( 31 \times 12 = 372 \) inches
We can set up a proportion using the heights and their respective shadows:
\[
\frac{\text{Myk's height}}{\text{Myk's shadow}} = \frac{\text{Flagpole's height}}{\text{Flagpole's shadow}}
\]
Let \( h \) be the height of the flagpole in inches. Therefore, we have:
\[
\frac{62}{84} = \frac{h}{372}
\]
Now we can cross-multiply to solve for \( h \):
\[
62 \times 372 = 84 \times h
\]
Calculating \( 62 \times 372 \):
\[
62 \times 372 = 23064
\]
So we have:
\[
23064 = 84h
\]
Now, divide both sides by 84 to isolate \( h \):
\[
h = \frac{23064}{84} \approx 274.0 \text{ inches}
\]
Now, to convert the height from inches to feet:
\[
\text{Height in feet} = \frac{274.0}{12} \approx 22.83 \text{ feet}
\]
Rounding to the nearest foot gives us \( 23 \) feet.
The correct answer is \( \boxed{23} \) feet.
Answered by
GPT-4o mini
You're welcome! If you have any more questions or need further assistance, feel free to ask. Have a great day! 😊
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.