Camila has a window that is 16 feet high from the ground, and she has a 20 foot ladder that she will place against the wall in such a way that the top of the ladder reaches the bottom of the window.

1 answer

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.