Camila needs to fix the window on the front of her house. The bottom of the

Question

window is 16 ft. from the ground. She only has a 20 ft. 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? (1 point)

Answer 1

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.