Question
A 25-foot-tall flag pole casts a shadow that is 18 feet long. Which of the following correctly uses the Pythagorean Theorem to sole for the distance from the top of the flag pole to the tip of its shawdow?(1 point)
Responses
308 feet
308 feet
30.8 feet
30.8 feet
17.3 feet
17.3 feet
43 feet
Responses
308 feet
308 feet
30.8 feet
30.8 feet
17.3 feet
17.3 feet
43 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 consider the flag pole and its shadow as forming a right triangle.
Here, the height of the flag pole represents one leg of the triangle (25 feet), the shadow represents the other leg (18 feet), and the distance from the top of the flag pole to the tip of its shadow represents the hypotenuse (let's denote it as \( c \)).
Using the Pythagorean Theorem:
\[
c^2 = a^2 + b^2
\]
where \( a = 25 \) feet (the height of the flag pole) and \( b = 18 \) feet (the length of the shadow).
Plugging in the values:
\[
c^2 = 25^2 + 18^2
\]
\[
c^2 = 625 + 324
\]
\[
c^2 = 949
\]
\[
c = \sqrt{949} \approx 30.8 \text{ feet}
\]
Therefore, the correct response is **30.8 feet**.
Here, the height of the flag pole represents one leg of the triangle (25 feet), the shadow represents the other leg (18 feet), and the distance from the top of the flag pole to the tip of its shadow represents the hypotenuse (let's denote it as \( c \)).
Using the Pythagorean Theorem:
\[
c^2 = a^2 + b^2
\]
where \( a = 25 \) feet (the height of the flag pole) and \( b = 18 \) feet (the length of the shadow).
Plugging in the values:
\[
c^2 = 25^2 + 18^2
\]
\[
c^2 = 625 + 324
\]
\[
c^2 = 949
\]
\[
c = \sqrt{949} \approx 30.8 \text{ feet}
\]
Therefore, the correct response is **30.8 feet**.