Camila needs to fix the window on the front of her house. The bottom of the window is 16 ft from the ground. She only has a 20ft ladder. How far from the base of the house should she set up the ladder so that the top of the ladder is exactly at the bottom of the window?

Answer 1

To find out how far from the base of the house Camila should set up the ladder, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the ladder, in this case) is equal to the sum of the squares of the lengths of the other two sides.

Let \( d \) be the distance from the base of the house to the base of the ladder (the horizontal distance), and the height of the window from the ground is given as \( 16 \) ft. The length of the ladder is \( 20 \) ft.

According to the Pythagorean theorem:

\[ \text{(Length of ladder)}^2 = \text{(Height from ground to window)}^2 + \text{(Distance from base of house)}^2 \]

Substituting the known values:

\[ 20^2 = 16^2 + d^2 \]

Calculating the squares:

\[ 400 = 256 + d^2 \]

To find \( d^2 \), we subtract \( 256 \) from both sides:

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

Now, taking the square root of both sides:

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

Therefore, Camila should set up the ladder 12 feet from the base of the house.