Question

If you place a 26-foot ladder against the top of a building and the bottom of the ladder is 20 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 distance from the base of the building to the bottom of the ladder form a right triangle, where:

- The length of the ladder is the hypotenuse (c = 26 feet).
- The distance from the bottom of the ladder to the building is one leg (a = 20 feet).
- The height of the building is the other leg (b), which we need to find.

According to the Pythagorean theorem:

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

Substituting the known values:

\[
26^2 = 20^2 + b^2
\]

Calculating the squares:

\[
676 = 400 + b^2
\]

To isolate \( b^2 \), we subtract 400 from both sides:

\[
676 - 400 = b^2
\]

\[
276 = b^2
\]

Next, we take the square root of both sides to solve for \( b \):

\[
b = \sqrt{276}
\]

Calculating the square root:

\[
b \approx 16.613
\]

Rounding to the nearest tenth of a foot:

\[
b \approx 16.6 \text{ feet}
\]

Thus, the height of the building is approximately **16.6 feet**.