Question

A ladder that is 22 feet long is leaning against a 15-foot tall wall. Label the photo with the correct side lengths based on the given information.

*Note, you will have to solve for the missing side.

(3 points)
Wall
Ladder
Ground

OPTIONS: 22 ft., 15 ft. 16.09 ft., 14 ft., and 7 ft.

Answer 1

To solve for the missing side length (the distance from the bottom of the ladder to the wall), we can use the Pythagorean theorem. The theorem states:

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

where:
- \( a \) is one leg of the triangle (height of the wall),
- \( b \) is the other leg of the triangle (distance from the wall to the bottom of the ladder), and
- \( c \) is the hypotenuse (length of the ladder).

Given:
- \( c = 22 \) feet (length of the ladder),
- \( a = 15 \) feet (height of the wall).

We need to find \( b \):

\[ 15^2 + b^2 = 22^2 \]
\[ 225 + b^2 = 484 \]
\[ b^2 = 484 - 225 \]
\[ b^2 = 259 \]
\[ b = \sqrt{259} \]
\[ b \approx 16.09 \text{ feet} \]

Now, we can label the parts based on the side lengths found.

- Wall: 15 ft (height)
- Ground: Approximately 16.09 ft (distance from the wall to the bottom of the ladder)
- Ladder: 22 ft (length)

So, based on the given information, the labeled photo should look like this:

- **Wall**: 15 ft
- **Ground**: Approximately 16.09 ft
- **Ladder**: 22 ft