A fence 3 feet tall runs parallel to a tall building at a distance of 7 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 is the hypotenuse, and the distance from the building to the fence is one of the sides. Let's denote the length of the ladder as L.
Using the Pythagorean theorem, we have:
L^2 = 3^2 + 7^2
Simplifying:
L^2 = 9 + 49
L^2 = 58
Taking the square root of both sides:
L ≈ √58
Therefore, the length of the shortest ladder that will reach from the ground over the fence to the wall of the building is approximately √58 feet.
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 represents the hypotenuse, and the fence and the distance from the building represent the other two sides of the right triangle.
Let's label the height of the fence as A (3 feet) and the distance from the building as B (7 feet). The length of the ladder, which is the hypotenuse, can be represented as C.
Using the Pythagorean theorem, we have the equation:
C^2 = A^2 + B^2
Plugging in the values we know:
C^2 = 3^2 + 7^2
C^2 = 9 + 49
C^2 = 58
To find the length of the ladder C, we take the square root of both sides:
C = √58
So, the length of the shortest ladder that will reach from the ground over the fence to the wall of the building is approximately 7.62 feet.