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
625 feet
625 feet
25 feet
25 feet
13.2 feet
13.2 feet
35 feet
Responses
625 feet
625 feet
25 feet
25 feet
13.2 feet
13.2 feet
35 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 height of the flag pole and the length of the shadow as forming a right triangle.
In this case:
- The height of the flag pole (one side of the triangle) = 20 feet
- The length of the shadow (the other side of the triangle) = 15 feet
- The distance from the top of the flag pole to the tip of the shadow (the hypotenuse) is what we are solving for.
Using the Pythagorean Theorem:
\[
a^2 + b^2 = c^2
\]
Where:
- \(a\) = 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
Now substituting the values:
\[
20^2 + 15^2 = c^2
\]
Calculating:
\[
400 + 225 = c^2
\]
\[
625 = c^2
\]
To find \(c\), take the square root of both sides:
\[
c = \sqrt{625} = 25 \text{ feet}
\]
Thus, the correct answer is:
**25 feet**
In this case:
- The height of the flag pole (one side of the triangle) = 20 feet
- The length of the shadow (the other side of the triangle) = 15 feet
- The distance from the top of the flag pole to the tip of the shadow (the hypotenuse) is what we are solving for.
Using the Pythagorean Theorem:
\[
a^2 + b^2 = c^2
\]
Where:
- \(a\) = 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
Now substituting the values:
\[
20^2 + 15^2 = c^2
\]
Calculating:
\[
400 + 225 = c^2
\]
\[
625 = c^2
\]
To find \(c\), take the square root of both sides:
\[
c = \sqrt{625} = 25 \text{ feet}
\]
Thus, the correct answer is:
**25 feet**