Question

The bottom of a ladder must be placed 5 ft. from a wall. The ladder is 12 feet long.


Based on the diagram, what is the distance in feet from the ground that the ladder reaches the wall? Round to the nearest tenth.

Answer 1

To find the height at which the ladder reaches the wall, we can use the Pythagorean theorem. Let's denote the following:

- The length of the ladder \( L = 12 \) feet (this is the hypotenuse).
- The distance from the wall \( d = 5 \) feet (this is one leg of the right triangle).
- The height of the ladder on the wall \( h \) (this is the other leg of the right triangle, which we want to find).

According to the Pythagorean theorem:

\[
L^2 = d^2 + h^2
\]

Substituting the known values:

\[
12^2 = 5^2 + h^2
\]

Calculating the squares:

\[
144 = 25 + h^2
\]

Now, isolate \( h^2 \):

\[
h^2 = 144 - 25
\]
\[
h^2 = 119
\]

Now, take the square root to find \( h \):

\[
h = \sqrt{119}
\]

Calculating \( \sqrt{119} \):

\[
h \approx 10.9087
\]

Rounding to the nearest tenth, we find:

\[
h \approx 10.9 \text{ feet}
\]

Thus, the distance from the ground that the ladder reaches the wall is approximately **10.9 feet**.