a 12ft ladder leans against the side of a house . the bottom of the ladder is 8ft from the side of the house how high is the top of the ladder from the ground
To find the height of the ladder from the ground, we can use the Pythagorean theorem.
According to the theorem, in a right-angled triangle, the square of the hypotenuse (the longest side, or 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. Let's call the height of the ladder h and the distance from the side of the house to the bottom of the ladder b.
We have:
h^2 = (8ft)^2 + b^2
h^2 = 64ft^2 + b^2
Now, we know the ladder is 12ft long, so the height and the base are related:
h^2 + b^2 = (12ft)^2
h^2 + b^2 = 144ft^2
Combining the two equations, we have:
64ft^2 + b^2 = 144ft^2
b^2 = 144ft^2 - 64ft^2
b^2 = 80ft^2
Taking the square root of both sides:
b = sqrt(80ft^2)
b = 8.94ft
Therefore, the top of the ladder is approximately 8.94ft from the ground.