To find out how far Camila should set up the ladder from the base of the house, we can use the Pythagorean theorem.
We know:
- The height of the window (the vertical leg of the triangle) is 16 ft.
- The length of the ladder (the hypotenuse of the triangle) is 20 ft.
Let \( x \) be the distance from the base of the house to the base of the ladder (the horizontal leg of the triangle).
According to the Pythagorean theorem:
\[ a^2 + b^2 = c^2 \]
Where:
- \( a \) is the height of the window (16 ft)
- \( b \) is the distance from the base of the house (x ft)
- \( c \) is the length of the ladder (20 ft)
Plugging in the values we have:
\[ 16^2 + x^2 = 20^2 \]
Calculating the squares:
\[ 256 + x^2 = 400 \]
Now, subtract 256 from both sides:
\[ x^2 = 400 - 256 \]
\[ x^2 = 144 \]
Taking the square root of both sides:
\[ x = 12 \]
Thus, Camila should set up the ladder 12 ft from the base of the house.