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 625 feet 625 feet 25 feet 25 feet 13.2 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.

In this scenario:

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

According to the Pythagorean Theorem:

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

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

Substituting the values:

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

Calculating each term:

\[ 400 + 225 = c^2 \]

\[ 625 = c^2 \]

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

\[ c = \sqrt{625} \]

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

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.