How far from the wall must you place a ladder of length 12m. if the ladder is to touch a point 10m above the ground?
a^2 + b^2 = c^2
10^2 + b^2 = 12^2
100 + b^2 = 144
b^2 = 44
b = 6.63 m
To determine how far the ladder must be placed from the wall, we can use the Pythagorean theorem, which states that in a right-angled 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 represents the hypotenuse, and the distance from the wall represents one of the other sides, while the distance from the ground represents the other side.
Let's call the distance from the wall "x".
According to the Pythagorean theorem:
x^2 + 10^2 = 12^2
Simplifying the equation:
x^2 + 100 = 144
Subtracting 100 from both sides:
x^2 = 44
Now, let's find the square root of both sides to get the value of "x":
√(x^2) = √44
x = √44
Calculating the square root of 44:
x ≈ 6.633
Therefore, the ladder must be placed approximately 6.633 meters from the wall.
To find out how far from the wall you must place the ladder, we can use the Pythagorean Theorem. The Pythagorean Theorem states that in 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 a right triangle with the wall and the ground. The length of the ladder is the hypotenuse, the distance from the wall to the point where the ladder touches the ground is one side, and the height of the ladder above the ground is the other side.
Let's label the distance from the wall to the point on the ground where the ladder touches as 'x.' We already know that the length of the ladder is 12m and the height of the ladder above the ground is 10m.
Therefore, according to the Pythagorean Theorem:
x^2 + 10^2 = 12^2
Simplifying the equation:
x^2 + 100 = 144
Subtracting 100 from both sides:
x^2 = 44
To find the value of x, we need to take the square root of both sides:
x = √44
Simplifying the square root of 44:
x ≈ 6.63
Therefore, you must place the ladder approximately 6.63 meters away from the wall.