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
25 feet
25 feet
625 feet
Responses
35 feet
35 feet
13.2 feet
13.2 feet
25 feet
25 feet
625 feet
Answers
GPT-4o mini
To find the distance from the top of the flag pole to the tip of its shadow, we can use the Pythagorean theorem. In this situation, the height of the flag pole is one leg of a right 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.
Let:
- \( a = \) height of the flag pole = 20 feet
- \( b = \) length of the shadow = 15 feet
- \( c = \) distance from the top of the flag pole to the tip of the shadow (the hypotenuse)
According to the Pythagorean theorem:
\[
c^2 = a^2 + b^2
\]
Substituting the values:
\[
c^2 = 20^2 + 15^2
\]
\[
c^2 = 400 + 225
\]
\[
c^2 = 625
\]
Now, take the square root of both sides:
\[
c = \sqrt{625} = 25
\]
Thus, the distance from the top of the flag pole to the tip of its shadow is **25 feet**.
So the correct response is:
**25 feet**.
Let:
- \( a = \) height of the flag pole = 20 feet
- \( b = \) length of the shadow = 15 feet
- \( c = \) distance from the top of the flag pole to the tip of the shadow (the hypotenuse)
According to the Pythagorean theorem:
\[
c^2 = a^2 + b^2
\]
Substituting the values:
\[
c^2 = 20^2 + 15^2
\]
\[
c^2 = 400 + 225
\]
\[
c^2 = 625
\]
Now, take the square root of both sides:
\[
c = \sqrt{625} = 25
\]
Thus, the distance from the top of the flag pole to the tip of its shadow is **25 feet**.
So the correct response is:
**25 feet**.