To find out how much farther up the building the ladder now reaches, we can use the Pythagorean theorem.
In the first scenario (Figure 1), the ladder, the base of the building, and the height reached by the ladder form a right triangle.
Let x be the height reached by the ladder in the first scenario.
Using the Pythagorean theorem, we have:
8^2 + x^2 = 16^2
64 + x^2 = 256
x^2 = 192
x ≈ 13.86 feet
Therefore, in the first scenario, the ladder reaches approximately 13.86 feet up the building.
In the second scenario (Figure 2), we move the ladder 4 feet closer to the base of the building. This means the base of the ladder is now 4 feet away from the building.
Let y be the increased height reached by the ladder in the second scenario.
Using the Pythagorean theorem again, we have:
4^2 + y^2 = 16^2
16 + y^2 = 256
y^2 = 240
y ≈ 15.49 feet
Therefore, in the second scenario, the ladder now reaches approximately 15.49 feet up the building.
To find out how much farther up the building the ladder now reaches, we subtract the height reached in the first scenario from the height reached in the second scenario:
15.49 - 13.86 ≈ 1.63 feet
Therefore, the ladder now reaches approximately 1.63 feet farther up the building than it did before the move.
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.
1 answer
1 answer