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

35 feet
35 feet

25 feet
25 feet

13.2 feet
13.2 feet

625 feet
625 feet

Answer 1

To find the distance from the top of the flag pole to the tip of its shadow, we can think of the flag pole and its shadow forming a right triangle. The height of the flag pole is one leg of the triangle, the length of the shadow is the other leg, and the distance we want to find is the hypotenuse.

We can use the Pythagorean Theorem, which states that in a right triangle:

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

where:
- \( a \) is one leg (the height of the pole, 20 feet),
- \( b \) is the other leg (the length of the shadow, 15 feet),
- \( c \) is the hypotenuse (the distance from the top of the flag pole to the tip of the shadow).

Plugging in the values:

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

Calculating each term:

\[ 20^2 = 400 \]
\[ 15^2 = 225 \]

Now add these:

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

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

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

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

Thus, the correct response is:

**25 feet**.