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
13.2 feet
13.2 feet
35 feet
35 feet
625 feet
625 feet
25 feet
Responses
13.2 feet
13.2 feet
35 feet
35 feet
625 feet
625 feet
25 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 scenario, we can consider a right triangle where:
- One leg is the height of the flag pole (20 feet)
- The other leg is the length of the shadow (15 feet)
- The hypotenuse (distance from the top of the flag pole to the tip of its shadow) is what we need to solve for.
Using the Pythagorean theorem:
\[ c^2 = a^2 + b^2 \]
where:
- \( c \) is the length of the hypotenuse,
- \( a \) is the height of the pole (20 feet),
- \( b \) is the length of the shadow (15 feet).
Plugging in the values:
\[
c^2 = 20^2 + 15^2
\]
\[
c^2 = 400 + 225
\]
\[
c^2 = 625
\]
Now, taking the square root of both sides:
\[
c = \sqrt{625} = 25 \text{ feet}
\]
Thus, the distance from the top of the flag pole to the tip of its shadow is **25 feet**.
The correct response is **25 feet**.
In this scenario, we can consider a right triangle where:
- One leg is the height of the flag pole (20 feet)
- The other leg is the length of the shadow (15 feet)
- The hypotenuse (distance from the top of the flag pole to the tip of its shadow) is what we need to solve for.
Using the Pythagorean theorem:
\[ c^2 = a^2 + b^2 \]
where:
- \( c \) is the length of the hypotenuse,
- \( a \) is the height of the pole (20 feet),
- \( b \) is the length of the shadow (15 feet).
Plugging in the values:
\[
c^2 = 20^2 + 15^2
\]
\[
c^2 = 400 + 225
\]
\[
c^2 = 625
\]
Now, taking the square root of both sides:
\[
c = \sqrt{625} = 25 \text{ feet}
\]
Thus, the distance from the top of the flag pole to the tip of its shadow is **25 feet**.
The correct response is **25 feet**.