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

35 feet
35 feet

25 feet
25 feet

13.2 feet
13.2 feet

625 feet

1 answer

To find the distance from the top of the flag pole to the tip of its shadow using the Pythagorean theorem, we can set up a right triangle where:

  • The height of the flag pole (adjacent side) is 20 feet.
  • The length of the shadow (base) is 15 feet.
  • The distance from the top of the flag pole to the tip of its shadow (hypotenuse) is what we want to find.

According to the Pythagorean theorem, we have:

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

where:

  • \(a = 20\) feet (height of the pole)
  • \(b = 15\) feet (length of the shadow)
  • \(c\) is the distance we want to find.

Plugging in the values:

\[ 20^2 + 15^2 = c^2 \] \[ 400 + 225 = c^2 \] \[ 625 = c^2 \]

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

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

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