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

625 feet
625 feet

25 feet
25 feet

35 feet
35 feet

13.2 feet

Answer 1

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

Let's denote the height of the flagpole as \( a = 20 \) feet, the length of the shadow as \( b = 15 \) feet, and the distance we want to find (the hypotenuse) as \( c \).

According to the Pythagorean Theorem:

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

Substituting the values:

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

Now, we take the square root of both sides 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**.