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

25 feet
25 feet

35 feet
35 feet

13.2 feet
13.2 feet

625 feet
625 feet

1 answer

To find the distance from the top of the flag pole to the tip of its shadow, we can use the Pythagorean Theorem.

Let's denote:

  • the height of the flag pole as one leg of the right triangle, which is 20 feet,
  • the length of the shadow as the other leg of the right triangle, which is 15 feet,
  • the distance from the top of the flag pole to the tip of its shadow as the hypotenuse.

According to the Pythagorean Theorem:

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

where \(a\) and \(b\) are the legs of the triangle, and \(c\) is the hypotenuse.

Plugging in the values we have:

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

Calculating the squares:

\[ 400 + 225 = c^2 \]

This results in:

\[ 625 = c^2 \]

Taking the square root of both sides to find \(c\):

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

So, the distance from the top of the flag pole to the tip of its shadow is 25 feet.

Therefore, the correct response is:

25 feet.