Question

Have you placed a 39 foot ladder against the top of a building in the bottom of the ladder is 31 feet from the bottom of the building. How tall is the building round to the nearest 10th of a foot?

Answer 1

To find the height of the building, we can use the Pythagorean theorem, which is applicable for right triangles. In this case, the building height represents one leg of the triangle, the distance from the base of the building to the bottom of the ladder represents the other leg, and the ladder itself represents the hypotenuse.

The Pythagorean theorem states:

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

Where:
- \(a\) is the height of the building (one leg),
- \(b\) is the distance from the bottom of the ladder to the building (other leg),
- \(c\) is the length of the ladder (hypotenuse).

From the problem:
- \(c = 39\) feet (length of the ladder),
- \(b = 31\) feet (distance from the bottom of the ladder to the building).

We need to find \(a\):

\[
a^2 + 31^2 = 39^2
\]

Calculating \(31^2\) and \(39^2\):

\[
31^2 = 961
\]
\[
39^2 = 1521
\]

Now substituting back into the equation:

\[
a^2 + 961 = 1521
\]

Subtracting 961 from both sides:

\[
a^2 = 1521 - 961
\]
\[
a^2 = 560
\]

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

\[
a = \sqrt{560}
\]
\[
a \approx 23.7 \text{ feet}
\]

Thus, the height of the building is approximately **23.7 feet** when rounded to the nearest tenth of a foot.