A ladder 32 ft long stands flat and vertical against the side of a building. How many feet must the bottom end be pulled away from the wall to cause the top end to lower by 4 ft?

Ladder distance solution. Raheel Farooqi A ladder 32 ft long stands flat and vertical against the side of a building. How many feet must the bottom end be pulled away from the wall to cause the top end to lower by 4 ft We can use the Pythagorean theorem to solve this problem. Let x be the distance that the bottom end of the ladder must be pulled away from the wall. Then we can form a right triangle with the ladder as the hypotenuse, the distance x as one leg, and the distance that the top end of the ladder lowers as the other leg. From the problem statement, we know that the ladder is 32 ft long and the top end of the ladder lowers by 4 ft. So the length of one leg of the right triangle is 4 ft. Using the Pythagorean theorem, we have: ladder^2 = x^2 + 4^2 Simplifying this equation, we get: 32^2 = x^2 + 4^2 1024 = x^2 + 16 x^2 = 1008 x ≈ 31.75 ft Therefore, the bottom end of the ladder must be pulled away from the wall by approximately 31.75 ft to cause the top end of the ladder to lower by 4 ft.