A ladder 5 meters long leans against a wall, reaching over the top of a box that is 1 meter on each side. The box is against the wall. What is the maximum height on the wall that the ladder can reach? The side view is:
Assume the wall is perpendicular to the floor. Use your calculator to find the maximum height to the nearest .01 meter.
4.84 m
To find the maximum height on the wall that the ladder can reach, we need to use the Pythagorean theorem. This theorem states that in a right-angled triangle, the square of the length of the hypotenuse (c, in this case, the ladder) is equal to the sum of the squares of the other two sides (a and b).
In this scenario, the ladder (c) is the hypotenuse, and the sides of the box are perpendicular to the wall, forming a right-angled triangle with the ladder. One side of the box is 1 meter, so each leg of the triangle adjacent to the wall will have a length of 1 meter.
We can set up the equation as follows:
c^2 = a^2 + b^2
Here, a = 1 meter and b = 1 meter. Let's plug these values into the equation:
c^2 = 1^2 + 1^2
c^2 = 1 + 1
c^2 = 2
To solve for c, we take the square root of 2:
c = √2
The ladder is 5 meters long, and it leans against the wall, so the maximum height it can reach on the wall is equal to the length of the ladder minus the height above the box.
Maximum height on the wall = ladder length - height above the box
Maximum height on the wall = 5 - 1 (box height)
Maximum height on the wall = 4 meters
Therefore, the maximum height on the wall that the ladder can reach is 4 meters.