Question

How long must a ladder be to reach the top of a 12-foot wall if the bottom of the ladder is placed 3 feet from the base of the wall?

What is the unknown information that could be found using the Pythagorean theorem?


What is the approximate length of the ladder needed, rounding to the nearest hundredth?

Answer 1

To find the length of the ladder needed to reach the top of a 12-foot wall when the bottom of the ladder is placed 3 feet from the base of the wall, we can use the Pythagorean theorem. The situation can be visualized as a right triangle, where:

- One leg of the triangle is the height of the wall (12 feet).
- The other leg is the horizontal distance from the wall (3 feet).
- The hypotenuse is the length of the ladder, which we are trying to find.

According to the Pythagorean theorem:

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

where:
- \(a\) is one leg (height of the wall, 12 feet),
- \(b\) is the other leg (distance from wall, 3 feet),
- \(c\) is the hypotenuse (length of the ladder).

Substituting the known values into the equation:

\[
12^2 + 3^2 = c^2
\]

Calculating the squares:

\[
144 + 9 = c^2
\]

Adding them together:

\[
153 = c^2
\]

Now, we take the square root to find the length of the ladder:

\[
c = \sqrt{153} \approx 12.369
\]

Rounding to the nearest hundredth, the length of the ladder needed is approximately **12.37 feet**.