Question

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

Answer 1

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.