Question

A ladder that is 21 feet long is propped against a building. The bottom of the ladder was placed 4 feet from the base of the building. How high up on the building does the ladder reach? Round the answer to the nearest tenth of a foot.
4.1 feet
17.0 feet
20.6 feet
21.4 feet

Answer 1

To determine how high the ladder reaches on the building, we can use the Pythagorean theorem. The ladder forms a right triangle with the ground and the wall of the building.

In this scenario:
- The length of the ladder is the hypotenuse (c = 21 feet).
- The distance from the base of the building to the bottom of the ladder is one leg of the triangle (a = 4 feet).
- The height at which the ladder touches the building is the other leg of the triangle (b).

According to the Pythagorean theorem:

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

Substituting in the known values:

\[
21^2 = 4^2 + b^2
\]

Calculating the squares:

\[
441 = 16 + b^2
\]

Next, we subtract 16 from both sides:

\[
441 - 16 = b^2
\]
\[
425 = b^2
\]

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

\[
b = \sqrt{425} \approx 20.6155
\]

Rounding this to the nearest tenth gives:

\[
b \approx 20.6 \text{ feet}
\]

Therefore, the height at which the ladder reaches the building is **20.6 feet**.