Question

If you place a 21-foot ladder against the top of a building and the bottom of the ladder is 12 feet from the bottom of the building, how tall is the building? Round to the nearest tenth of a foot.

Answer 1

To find the height of the building, we can use the Pythagorean theorem. The ladder, the height of the building, and the ground form a right triangle, where:

- \( a \) is the height of the building (which we want to find),
- \( b \) is the distance from the base of the building to the bottom of the ladder (12 feet), and
- \( c \) is the length of the ladder (21 feet).

The Pythagorean theorem states:

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

Substituting the known values into the equation:

\[
a^2 + 12^2 = 21^2
\]

Calculating \( 12^2 \) and \( 21^2 \):

\[
12^2 = 144
\]
\[
21^2 = 441
\]

Now substituting these values back into the equation:

\[
a^2 + 144 = 441
\]

Next, isolate \( a^2 \):

\[
a^2 = 441 - 144
\]
\[
a^2 = 297
\]

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

\[
a = \sqrt{297}
\]

Calculating \( \sqrt{297} \):

\[
a \approx 17.2
\]

Thus, the height of the building is approximately \( \boxed{17.2} \) feet, rounded to the nearest tenth of a foot.