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 625 feet 625 feet 25 feet 25 feet 35 feet

Answer 1

To find the distance from the top of the flag pole to the tip of its shadow, we can visualize 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 is the distance from the top of the flag pole to the tip of the shadow.

Using the Pythagorean Theorem, which states:

\[
a^2 + b^2 = c^2
\]

where \(c\) is the hypotenuse, and \(a\) and \(b\) are the other two sides, we can set up the equation:

\[
20^2 + 15^2 = c^2
\]

Calculating \(20^2\) and \(15^2\):

\[
20^2 = 400
\]
\[
15^2 = 225
\]

Adding these together:

\[
400 + 225 = 625
\]

Now, we take the square root to find \(c\):

\[
c = \sqrt{625} = 25
\]

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**.