A
12
-
ft
ladder leans against the side of a house. The bottom of the ladder is
6 ft
from the side of the house. How high is the top of the ladder from the ground? If necessary, round your answer to the nearest tenth.
6^2 + h^2 = 12^2
so, what is h?
The answer is 10
To solve this problem, we can use the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the ladder is the hypotenuse, and one side is the distance from the house to the ladder base, which is 6 ft. Let's call the other side "h" for height.
So, using the Pythagorean Theorem:
12^2 = 6^2 + h^2
Simplifying:
144 = 36 + h^2
Subtracting 36 from both sides:
108 = h^2
Taking the square root of both sides:
h = √108
Calculating the square root:
h ≈ 10.4 ft
Therefore, the top of the ladder is approximately 10.4 ft from the ground.
To find the height of the top of the ladder from the ground, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the ladder forms a right triangle with the ground and the side of the house. The ladder is the hypotenuse, and the distance from the bottom of the ladder to the side of the house is one of the legs.
Given that the bottom of the ladder is 6 ft from the side of the house (one leg) and the ladder itself is 12 ft long (the hypotenuse), we can find the height of the ladder (the other leg).
Using the Pythagorean theorem, we have:
12^2 = 6^2 + height^2
Simplifying the equation:
144 = 36 + height^2
Subtracting 36 from both sides:
height^2 = 144 - 36
height^2 = 108
Taking the square root of both sides:
height = √108
Calculating the square root of 108 gives us:
height ≈ 10.39
Therefore, the height of the top of the ladder from the ground is approximately 10.39 ft.