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

17.3 feet
17.3 feet

308 feet
308 feet

43 feet
43 feet

30.8 feet

Answer 1

To find the distance from the top of the flag pole to the tip of its shadow, we can use the Pythagorean Theorem. The flag pole, the shadow, and the distance from the top of the flag pole to the tip of the shadow form a right triangle.

In this case, the height of the flag pole is one leg of the right triangle (25 feet), the length of the shadow is the other leg (18 feet), and the distance from the top of the flag pole to the tip of the shadow is the hypotenuse (which we will denote as \(c\)).

According to the Pythagorean Theorem:

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

Where:
- \(c\) is the hypotenuse
- \(a\) is the height of the flag pole (25 feet)
- \(b\) is the length of the shadow (18 feet)

Plugging in the values:

\[
c^2 = 25^2 + 18^2
\]

Calculating the squares:

\[
c^2 = 625 + 324
\]

\[
c^2 = 949
\]

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

\[
c = \sqrt{949} \approx 30.8 \text{ feet}
\]

So the distance from the top of the flag pole to the tip of its shadow is approximately 30.8 feet.

The correct answer is:

30.8 feet