To determine how far away from the wall the base of the ladder should be placed, we can use the Pythagorean theorem. The ladder forms a right triangle with the wall and the ground. In this triangle:
- The height of the window (16 feet) is one leg of the triangle (the vertical side).
- The distance from the wall to the base of the ladder is the other leg of the triangle (the horizontal side).
- The length of the ladder (20 feet) is the hypotenuse.
Using the Pythagorean theorem:
\[ a^2 + b^2 = c^2 \]
where:
- \(a\) is the height of the window (16 feet),
- \(b\) is the distance from the wall to the base of the ladder,
- \(c\) is the length of the ladder (20 feet).
Now, substituting the known values into the equation:
\[ 16^2 + b^2 = 20^2 \]
Calculating the squares:
\[ 256 + b^2 = 400 \]
Now, isolate \(b^2\):
\[ b^2 = 400 - 256 \]
\[ b^2 = 144 \]
Taking the square root of both sides to find \(b\):
\[ b = \sqrt{144} = 12 \]
Therefore, Camila should place the base of the ladder 12 feet away from the wall.