Question
A 20-foot-tall flag pole casts a shadow that is 15 feet long. Which of the following correctly uses the Pythagorean Theorem to solve for the distance from the top of the flag pole to the tip of its shadow?(1 point)
Responses
35 feet
35 feet
13.2 feet
13.2 feet
625 feet
625 feet
25 feet
Responses
35 feet
35 feet
13.2 feet
13.2 feet
625 feet
625 feet
25 feet
Answers
GPT-4o mini
To find the distance from the top of the flag pole to the tip of its shadow, we can visualize a right triangle where:
- One side is the height of the flag pole, which is 20 feet.
- The other side is the length of the shadow, which is 15 feet.
- The distance we want to find is the hypotenuse of this triangle.
According to the Pythagorean Theorem, we have:
\[
c^2 = a^2 + b^2
\]
where \(c\) is the length of the hypotenuse, \(a\) is the height of the flag pole, and \(b\) is the length of the shadow.
Substituting in our numbers:
\[
c^2 = 20^2 + 15^2
\]
Calculating the squares:
\[
c^2 = 400 + 225
\]
Adding these together:
\[
c^2 = 625
\]
Now, take the square root to find \(c\):
\[
c = \sqrt{625} = 25 \text{ feet}
\]
So the correct answer is:
**25 feet**
- One side is the height of the flag pole, which is 20 feet.
- The other side is the length of the shadow, which is 15 feet.
- The distance we want to find is the hypotenuse of this triangle.
According to the Pythagorean Theorem, we have:
\[
c^2 = a^2 + b^2
\]
where \(c\) is the length of the hypotenuse, \(a\) is the height of the flag pole, and \(b\) is the length of the shadow.
Substituting in our numbers:
\[
c^2 = 20^2 + 15^2
\]
Calculating the squares:
\[
c^2 = 400 + 225
\]
Adding these together:
\[
c^2 = 625
\]
Now, take the square root to find \(c\):
\[
c = \sqrt{625} = 25 \text{ feet}
\]
So the correct answer is:
**25 feet**