To determine how far Camila should set up the ladder from the base of the house, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. The formula is:
\[ a^2 + b^2 = c^2 \]
In this scenario:
- \( c \) is the length of the ladder, which is 20 ft.
- \( b \) is the height from the ground to the bottom of the window, which is 16 ft.
- \( a \) is the distance from the base of the house to the bottom of the ladder (the distance we need to find).
Using the Pythagorean theorem:
\[ a^2 + b^2 = c^2 \] \[ a^2 + (16)^2 = (20)^2 \] \[ a^2 + 256 = 400 \]
Now, subtract 256 from both sides:
\[ a^2 = 400 - 256 \] \[ a^2 = 144 \]
Next, take the square root of both sides to find \( a \):
\[ a = \sqrt{144} \] \[ a = 12 \]
Therefore, Camila should set up the ladder 12 ft from the base of the house.