a ladder 6 meters long leans against a wall. It rests on the ground 1 meter away from the wall. How high on the wall does the ladder rest?
a^2 + b^2 = c^2
a^2 + 1^2 = 6^2
a^2 + 1 = 36
a^2 = 35
a = 5.92 meters
A famous Greek once proved this:
On a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs.
C^2=a^2+b^2
here, c is 6
a is 1
solve for b.
Four
To find out how high on the wall the ladder rests, we can use the Pythagorean theorem. The theorem states that in a right-angled 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 the hypotenuse of the right-angled triangle. The distance between the ladder and the wall forms one side of the triangle, and the height on the wall where the ladder rests forms the other side.
Let's denote the height on the wall as 'h'. We can set up the equation as follows:
(1 meter)^2 + h^2 = (6 meters)^2
1 + h^2 = 36
h^2 = 36 - 1
h^2 = 35
Taking the square root of both sides, we find:
h ≈ √35
Therefore, the ladder rests approximately at a height of √35 meters on the wall.