A 12 foot ladder leans against the side of a house the bottom of the ladder is 8 feet from the side of the house how high is the top of the ladder from the ground
Pythagorean Theorem:
a^2 + b^2 = c^2
8^2 + b^2 = 12^2
64 + b^2 = 144
b^2 = 80
b = 8.9 feet
Is there an answer for 10 feet instead of 8 feet?
8.9
To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the ladder forms the hypotenuse, and the distance from the house to the base of the ladder forms one of the sides. Let's call the height of the ladder h and the distance from the house to the base d.
According to the problem, the length of the ladder (hypotenuse) is 12 feet, and the distance from the house to the base is 8 feet.
Applying the Pythagorean theorem, we have:
12^2 = 8^2 + h^2
Simplifying, we get:
144 = 64 + h^2
Subtracting 64 from both sides, we have:
80 = h^2
To find h, we take the square root of both sides:
√80 ≈ 8.94
Therefore, the top of the ladder is approximately 8.94 feet from the ground.