Question

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.

Answer 1

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**.