A fence 4 feet tall runs parallel to a tall building at a distance of 5 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?

Two approaches to the same problem, one using trig, the other using only algebra.

Just change the numbers.

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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 longest side) is equal to the sum of the squares of the other two sides.

In this case, the ladder represents the hypotenuse, the fence is one of the shorter sides, and the distance from the fence to the building is the other shorter side.

Let's call the length of the ladder "L". According to the Pythagorean theorem, we have:

L^2 = fence^2 + distance^2

The fence is 4 feet tall, so fence^2 = 4^2 = 16.

The distance from the fence to the building is 5 feet, so distance^2 = 5^2 = 25.

Now we can substitute these values into the equation:

L^2 = 16 + 25
L^2 = 41

To find L, we need to take the square root of both sides of the equation:

L = √41

So, the length of the shortest ladder that will reach from the ground over the fence to the wall of the building is approximately equal to √41 feet.