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 30.8 feet 30.8 feet 17.3 feet 17.3 feet 43 feet 43 feet 308 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 and its shadow form a right triangle, where:
- The height of the flagpole is one leg (25 feet),
- The length of the shadow is the other leg (18 feet),
- The distance from the top of the flagpole to the tip of the shadow is the hypotenuse.
According to the Pythagorean Theorem:
\[
a^2 + b^2 = c^2
\]
Where:
- \(a\) is the height of the flagpole (25 feet),
- \(b\) is the length of the shadow (18 feet),
- \(c\) is the distance from the top of the flagpole to the tip of the shadow.
Now we can plug in the values:
\[
25^2 + 18^2 = c^2
\]
Calculating the squares:
\[
625 + 324 = c^2
\]
Adding them together:
\[
949 = c^2
\]
Now take the square root to find \(c\):
\[
c = \sqrt{949} \approx 30.8 \text{ feet}
\]
So the correct distance from the top of the flagpole to the tip of its shadow is approximately **30.8 feet**.
- The height of the flagpole is one leg (25 feet),
- The length of the shadow is the other leg (18 feet),
- The distance from the top of the flagpole to the tip of the shadow is the hypotenuse.
According to the Pythagorean Theorem:
\[
a^2 + b^2 = c^2
\]
Where:
- \(a\) is the height of the flagpole (25 feet),
- \(b\) is the length of the shadow (18 feet),
- \(c\) is the distance from the top of the flagpole to the tip of the shadow.
Now we can plug in the values:
\[
25^2 + 18^2 = c^2
\]
Calculating the squares:
\[
625 + 324 = c^2
\]
Adding them together:
\[
949 = c^2
\]
Now take the square root to find \(c\):
\[
c = \sqrt{949} \approx 30.8 \text{ feet}
\]
So the correct distance from the top of the flagpole to the tip of its shadow is approximately **30.8 feet**.