A 12 foot ladder leans against the side of a house the bottom of the ladder is 7 feet from the side of the house how high is the top of the ladder from the ground
To find the height of the top of the ladder from the ground, you 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 forms the hypotenuse, and the distances from the bottom of the ladder to the house and the height from the ground form the other two sides.
Let's denote the height from the ground to the top of the ladder as h. We already know that the distance from the bottom of the ladder to the house is 7 feet.
Using the Pythagorean theorem, we can write:
(7)^2 + h^2 = (12)^2
Simplifying the equation, we have:
49 + h^2 = 144
Now, we can isolate h^2 by subtracting 49 from both sides:
h^2 = 144 - 49
h^2 = 95
To find the value of h, we take the square root of both sides:
h = √95
Using a calculator, we find that the square root of 95 is approximately 9.75.
Therefore, the top of the ladder is approximately 9.75 feet from the ground.
To find the height of the top of the ladder from the ground, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) 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. We know that the bottom of the ladder (the base) is 7 feet, and the ladder itself (the hypotenuse) is 12 feet. Let's call the height of the ladder "h".
Using the Pythagorean theorem, we have:
7^2 + h^2 = 12^2
Simplifying:
49 + h^2 = 144
Subtracting 49 from both sides:
h^2 = 144 - 49
h^2 = 95
To find the height h, we need to take the square root of both sides:
√(h^2) = √95
h ≈ √95
h ≈ 9.75
Therefore, the top of the ladder is approximately 9.75 feet from the ground.
the ladder, the ground, and the side of the house form a right triangle
the ladder is the hypotenuse
use Pythagoras to find the height of the top of the ladder ... a^2 + b^2 = c^2