Question

A 10-foot-tall ladder rests against an 8-foot wall. The wall and ground form a 90-degree angle.


How many feet away from the wall is the bottom of the ladder?

Answer 1

To solve this problem, we can visualize it as a right triangle where:

- The height of the wall forms one leg of the triangle (8 feet).
- The distance from the base of the wall to the bottom of the ladder forms the other leg (let's call this distance \( x \)).
- The ladder itself forms the hypotenuse of the triangle (10 feet).

We can use the Pythagorean theorem, which states that in a right triangle:

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

where \( a \) and \( b \) are the legs of the triangle and \( c \) is the hypotenuse.

In our situation:

- \( a = 8 \) feet (height of the wall),
- \( b = x \) feet (distance from the wall),
- \( c = 10 \) feet (length of the ladder).

We can substitute the values into the Pythagorean theorem:

\[
8^2 + x^2 = 10^2
\]

Calculating the squares:

\[
64 + x^2 = 100
\]

Next, we want to isolate \( x^2 \):

\[
x^2 = 100 - 64
\]
\[
x^2 = 36
\]

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

\[
x = \sqrt{36}
\]
\[
x = 6
\]

Thus, the bottom of the ladder is **6 feet** away from the wall.