The ladder in figure 2 reaches 3.2 feet further up than the ladder in figure 1.
Step-by-step explanation:
Step 1:
In both the given figures, the ladder, the wall and the floor form a right-angled triangle. The floor is the adjacent side, the wall is the opposite side and the ladder is the hypotenuse.
According to the Pythagorean theorem,
[tex]a^{2}+b^{2}=c^{2}[/tex], where c is the length of the hypotenuse while a and b are the lengths of the other two sides.
Step 2:
For the ladder in figure 1, assume the distance from the floor to the ladder's top is x feet. So a = x, b = 8 and c = 10 (hypotenuse).
[tex]a^{2}+b^{2}=c^{2}[/tex], [tex]x^{2}+8^{2}=10^{2}[/tex], [tex]x^{2}=100-64=36, x=\sqrt{36}=6 \text { feet }[/tex].
So the distance between the floor and the ladder's top is 6 feet.
Step 3:
For the ladder in figure 2, assume the distance between the floor and the ladder's top is y feet. So a = y, b = 4 and c = 10 (hypotenuse).
[tex]a^{2}+b^{2}=c^{2}[/tex], [tex]y^{2}+4^{2}=10^{2}[/tex], [tex]y^{2}=100-16=48, x=\sqrt{84}=9.1651 \text { feet }[/tex].
So the distance between the floor and the ladder's top is 9.1651 feet.
Step 4:
The difference in heights = The wall height in figure 2 - the wall height in figure 1.
The difference in heights = 9.1651 feet - 6 feet = 3.1651 feet.
Rounding this off to the nearest tenth of a foot, we get 3.2 feet.
