A fence 5 feet tall runs parallel to a tall building at a distance of 3 feet from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?
To find the length of the shortest ladder that will reach from the ground over the fence to the wall of the building, 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 will form the hypotenuse of a right triangle, while the horizontal distance from the fence to the wall will be one of the legs.
Let's label the sides of the right triangle:
- The height of the fence is 5 feet, so this will be one leg of the triangle.
- The distance from the fence to the building is 3 feet, so this will be the other leg of the triangle.
- The length of the ladder, which we need to find, will be the hypotenuse.
By applying the Pythagorean Theorem, we have:
Length of the ladder^2 = Length of fence^2 + Distance from fence to building^2
Length of the ladder^2 = (5 feet)^2 + (3 feet)^2
Length of the ladder^2 = 25 feet^2 + 9 feet^2
Length of the ladder^2 = 34 feet^2
To find the length of the ladder, we need to take the square root of both sides of the equation.
Length of the ladder = √(34 feet^2)
Length of the ladder ≈ 5.83 feet
Therefore, the length of the shortest ladder that will reach from the ground over the fence to the wall of the building is approximately 5.83 feet.