The ladder initially slipped down approximately 295.84 cm. After moving the foot 70 cm further away, the final position resulted in a slip of approximately 8.27 cm down the wall.
The scenario involves a right-angled triangle formed by a 3 m ladder, a vertical wall, and the ground. Initially, the ladder, the hypotenuse, measures 3 meters, with its foot 50 cm away from the wall's base. Let's denote the distance down the wall as "x".
By the Pythagorean theorem, initially:
x^2 + 50^2 = 300^2
As the ladder slips, the foot moves 70 cm further away, making the new distance 120 cm:
(x + 70)^2 + 50^2 = 300^2
Solving these equations gives "x".
Firstly, solving the initial equation:
x^2 + 50^2 = 300^2
x^2 + 2500 = 90000
x^2 = 87500
x is approximately 295.84
Now, solving the final equation:
(x + 70)^2 + 50^2 = 90000
(295.84 + 70)^2 + 2500 = 90000
x^2 + 4900 + 2500 = 90000
x^2 + 7400 = 90000
x^2 = 82600
x is approximately 287.57
The ladder slipped approximately 295.84 - 287.57 ≈ 8.27 cm down the wall.