Question

camila needs to fix the window on the front of her house. the bottom of the window is 16ft from the ground, and only has a 20ft ladder. how far would she need to set the ladder to be at the base of the window

Answer 1

To determine how far from the wall Camila needs to set the base of the ladder, we can use the Pythagorean theorem. In this scenario, the ladder forms a right triangle with the wall and the ground.

We have:
- The height of the window (which is the vertical side of the triangle) = 16 ft
- The length of the ladder (which is the hypotenuse of the triangle) = 20 ft
- We'll call the distance from the base of the ladder to the wall (the horizontal side of the triangle) \( x \).

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 wall (we want to find this, so it’s \( x \))
- \( c \) is the length of the ladder (20 ft)

Substituting the known values into the equation:

\[
(16)^2 + x^2 = (20)^2
\]

Calculating the squares:

\[
256 + x^2 = 400
\]

Now, subtract 256 from both sides to solve for \( x^2 \):

\[
x^2 = 400 - 256
\]
\[
x^2 = 144
\]

Now, take the square root of both sides to find \( x \):

\[
x = \sqrt{144}
\]
\[
x = 12
\]

So, Camila would need to set the base of the ladder **12 feet** away from the wall to reach the window.