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
625 feet
625 feet
13.2 feet
13.2 feet
25 feet
25 feet
35 feet
Responses
625 feet
625 feet
13.2 feet
13.2 feet
25 feet
25 feet
35 feet
Answers
GPT-4o mini
To find the distance from the top of the flagpole to the tip of its shadow, we can use the Pythagorean Theorem. The flagpole, its shadow, and the line from the top of the flagpole to the tip of the shadow form a right triangle.
Let's denote:
- The height of the flagpole is \(a = 20\) feet.
- The length of the shadow is \(b = 15\) feet.
- The distance from the top of the flagpole to the tip of the shadow is \(c\).
According to the Pythagorean Theorem:
\[
c^2 = a^2 + b^2
\]
Substituting the values:
\[
c^2 = 20^2 + 15^2
\]
Calculating \(20^2\) and \(15^2\):
\[
20^2 = 400
\]
\[
15^2 = 225
\]
Now, add these two results:
\[
c^2 = 400 + 225 = 625
\]
Now, take the square root of both sides to find \(c\):
\[
c = \sqrt{625} = 25 \text{ feet}
\]
Therefore, the correct answer is **25 feet**.
Let's denote:
- The height of the flagpole is \(a = 20\) feet.
- The length of the shadow is \(b = 15\) feet.
- The distance from the top of the flagpole to the tip of the shadow is \(c\).
According to the Pythagorean Theorem:
\[
c^2 = a^2 + b^2
\]
Substituting the values:
\[
c^2 = 20^2 + 15^2
\]
Calculating \(20^2\) and \(15^2\):
\[
20^2 = 400
\]
\[
15^2 = 225
\]
Now, add these two results:
\[
c^2 = 400 + 225 = 625
\]
Now, take the square root of both sides to find \(c\):
\[
c = \sqrt{625} = 25 \text{ feet}
\]
Therefore, the correct answer is **25 feet**.