If you place a 32-foot ladder against the top of a 23-foot building, how many feet will the bottom of the ladder be from the bottom of the building? Round to the nearest tenth of a foot.

1 answer

We can use the Pythagorean theorem to solve this problem. The ladder, the height of the building, and the distance from the bottom of the ladder to the bottom of the building form a right triangle.

Let:

  • \( c \) = length of the ladder = 32 feet (hypotenuse),
  • \( a \) = height of the building = 23 feet (one leg of the triangle),
  • \( b \) = distance from the bottom of the ladder to the building (the other leg of the triangle).

According to the Pythagorean theorem: \[ c^2 = a^2 + b^2 \]

We can plug in the values we have: \[ 32^2 = 23^2 + b^2 \]

Calculating the squares: \[ 1024 = 529 + b^2 \]

Now, we can isolate \( b^2 \): \[ b^2 = 1024 - 529 \] \[ b^2 = 495 \]

Next, we take the square root of both sides to find \( b \): \[ b = \sqrt{495} \]

Calculating the square root: \[ b \approx 22.271 \]

Rounding to the nearest tenth: \[ b \approx 22.3 \]

Thus, the distance from the bottom of the ladder to the bottom of the building is approximately \( \boxed{22.3} \) feet.