Question

2

Numeric
1 point



Question at position 2
A 41-foot ladder is place against a vertical wall of an apartment building. The base of the ladder is 9 feet from the base of the apartment building.



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How many feet up the apartment building is the top of the ladder?

Answer 1

To find out how high up the apartment building the top of the ladder reaches, we can use the Pythagorean theorem. This theorem states that in a right-angled triangle:

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

where \(c\) is the length of the hypotenuse (the ladder, in this case), and \(a\) and \(b\) are the lengths of the other two sides.

In this problem:
- The length of the ladder (hypotenuse, \(c\)) = 41 feet
- The distance from the wall to the base of the ladder (\(a\)) = 9 feet
- The height of the ladder on the wall (\(b\)) is what we're trying to find.

Plugging in the known values:

\[
9^2 + b^2 = 41^2
\]

Calculating \(9^2\) and \(41^2\):

\[
81 + b^2 = 1681
\]

Now, subtract 81 from both sides to isolate \(b^2\):

\[
b^2 = 1681 - 81
\]
\[
b^2 = 1600
\]

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

\[
b = \sqrt{1600}
\]
\[
b = 40
\]

Thus, the top of the ladder reaches **40 feet** up the apartment building.