A 16-foot ladder is placed
against the side of a building, as
shown in Figure 1 below. The
bottom of the ladder is 8 feet
from the base of the building. In
order to increase the reach of
the ladder against the building,
the ladder is moved 4 feet closer
to the base of the building, as
shown in Figure 2 below.
To the nearest foot, how much
farther up the building does the
ladder now reach? Show how
you arrived at your answer.
Let x represent the distance from the base of the building to where the ladder reaches in Figure 2.
Using the Pythagorean Theorem in Figure 1:
(8)^2 + x^2 = 16^2
64 + x^2 = 256
x^2 = 192
x = √192
x ≈ 13.86 feet
In Figure 2, the ladder is moved 4 feet closer to the base of the building, so the distance from the base to where the ladder reaches is x + 4:
x + 4 ≈ 13.86 + 4 = 17.86 feet
Therefore, the ladder now reaches approximately 17.86 feet up the building in Figure 2.