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
25 feet
25 feet
35 feet
35 feet
625 feet
625 feet
13.2 feet
Responses
25 feet
25 feet
35 feet
35 feet
625 feet
625 feet
13.2 feet
Answers
GPT-4o mini
To solve for the distance from the top of the flag pole to the tip of its shadow using the Pythagorean Theorem, we can visualize this situation as a right triangle. The height of the flag pole is one leg of the triangle, the length of the shadow is the other leg, and the distance from the top of the flag pole to the tip of the shadow is the hypotenuse.
Given:
- Height of the flag pole (one leg) = 20 feet
- Length of the shadow (other leg) = 15 feet
According to the Pythagorean Theorem:
\[
c^2 = a^2 + b^2
\]
where \(c\) is the hypotenuse, \(a\) is one leg (20 feet), and \(b\) is the other leg (15 feet). Plugging in the values:
\[
c^2 = 20^2 + 15^2
\]
\[
c^2 = 400 + 225
\]
\[
c^2 = 625
\]
\[
c = \sqrt{625}
\]
\[
c = 25 \text{ feet}
\]
So the correct response is:
**25 feet**
Given:
- Height of the flag pole (one leg) = 20 feet
- Length of the shadow (other leg) = 15 feet
According to the Pythagorean Theorem:
\[
c^2 = a^2 + b^2
\]
where \(c\) is the hypotenuse, \(a\) is one leg (20 feet), and \(b\) is the other leg (15 feet). Plugging in the values:
\[
c^2 = 20^2 + 15^2
\]
\[
c^2 = 400 + 225
\]
\[
c^2 = 625
\]
\[
c = \sqrt{625}
\]
\[
c = 25 \text{ feet}
\]
So the correct response is:
**25 feet**