A 11 feet ladder is placed against a building. The bottom of the ladder is 8 feet away from the building. How many feet high is the top of the ladder?
Using the Pythagorean theorem, we can find the height of the ladder by calculating the length of the hypotenuse.
The hypotenuse (c) squared is equal to the sum of the squares of the other two sides (a and b):
c^2 = a^2 + b^2
Given that the bottom of the ladder is 8 feet away from the building, we have the following values:
a = 8 feet (distance from the bottom of the ladder to the building)
c = 11 feet (length of the ladder)
Substituting the values into the equation, we have:
11^2 = 8^2 + b^2
121 = 64 + b^2
b^2 = 121 - 64
b^2 = 57
Taking the square root of both sides, we get:
b = √57
Therefore, the top of the ladder is approximately 7.55 feet high.
To find the height of the top of the ladder, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the ladder represents the hypotenuse, the distance from the building to the bottom of the ladder represents one side, and the height we want to find represents the other side.
Let's call the height of the top of the ladder "h". According to the Pythagorean theorem:
h^2 = 11^2 - 8^2
Simplifying this equation:
h^2 = 121 - 64
h^2 = 57
To find h, we take the square root of both sides of the equation:
h = √57
Therefore, the height of the top of the ladder is approximately 7.55 feet.