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