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.

make sure to pay attention and be right

1 answer

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

Here, we can define:

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

According to the Pythagorean theorem:

\[ a^2 + b^2 = c^2 \]

Substituting the values we know:

\[ 23^2 + b^2 = 32^2 \]

Calculating the squares:

\[ 529 + b^2 = 1024 \]

Now, subtract 529 from both sides:

\[ b^2 = 1024 - 529 \] \[ b^2 = 495 \]

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

\[ b = \sqrt{495} \]

Calculating \( \sqrt{495} \):

\[ \sqrt{495} \approx 22.3 \]

Thus, the distance from the bottom of the ladder to the building is approximately 22.3 feet, when rounded to the nearest tenth of a foot.