A -12 ft ladder leans against the side of a house. The bottom of the ladder is 7 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.
This forms a right triangle where the ladder is the hypotenuse, the distance from the side of the house is the adjacent side, and the height is the opposite side.
Let's use the Pythagorean theorem to solve for the height:
height^2 + (adjacent side)^2 = hypotenuse^2
height^2 + 7ft^2 = 12ft^2
height^2 + 49ft^2 = 144ft^2
height^2 = 144ft^2 - 49ft^2
height^2 = 95ft^2
height ≈ √95ft ≈ 9.7ft
The top of the ladder is approximately 9.7 feet 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 for 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 the hypotenuse of a right triangle, and the distance from the house to the bottom of the ladder forms one of the other sides.
Let's call the height of the top of the ladder from the ground "h".
According to the problem, the bottom of the ladder is 7 ft from the side of the house, so one side of the triangle is 7 ft.
We can use the Pythagorean theorem to find the length of the ladder:
h^2 = (-12)^2 + 7^2
h^2 = 144 + 49
h^2 = 193
To find the height of the top of the ladder from the ground, we need to take the square root of both sides:
√h^2 = √193
h ≈ 13.9
Therefore, the top of the ladder is approximately 13.9 ft from the ground.
To find the height of the top of the ladder from the ground, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the ladder forms a right triangle with the side of the house and the ground. The ladder is the hypotenuse, and its length is given as -12 ft. The distance from the bottom of the ladder to the house is the adjacent side, given as 7 ft. The height of the ladder from the ground is the opposite side, which we need to find.
Let's call the height of the ladder (opposite side) 'h'. According to the Pythagorean theorem, we have:
h^2 = (-12)^2 - 7^2
Simplifying this equation, we get:
h^2 = 144 - 49
h^2 = 95
Now, we need to find the square root of both sides to solve for 'h':
h = √95
Using a calculator, we find that √95 is approximately 9.7.
Therefore, the height of the top of the ladder from the ground is approximately 9.7 feet.