A 25 ft ladder leans up against the side of a house, the base of the ladder a distance 4 ft from the wall. If the ladder is moved out by 4 feet, how far down the wall will the top of the ladder move?

Answer 1

If I understood the problem correctly, the expression the "ladder moved out by 4 ft refers to the motion of the ladder's base.

In first case, when the ladder near the wall, we know that its length is 25 ft and 4 ft distance from the wall. We can use the Pythagoras theorem to find the distance of the top of the ladder from the floor in vertical direction.

c² = a² + b²

In our case c = 25, a = 4, then the distance of the top of the ladder from the floor in vertical direction, b, is:

b = √ ( c² - a²)

Plugging in the numbers, we get

b = √ ( 25² - 4²) = √ (625 - 16) = 24.7 (ft)

When the base of the ladder moves extra 4 ft, new value of a is 8 ft. Applying in a similar way the Pythagoras theorem, we have new value of b

b = √ (625 - 64) = 23.7 ft

The difference between old and new values of b gives us the answer to the question of how far down the wall the top of the ladder moved.

Δ b = 24.7 ft - 23.7 ft = 1 ft

Answer: 1 ft