This problem involves applying the Pythagorean theorem to calculate how far the ladder slipped down the wall.

Step 1: Initial position

The ladder is 3 meters (300 cm) long, and the distance of the base of the ladder from the wall is 50 cm. Using the Pythagorean theorem: $\text{Length of ladder}^2 = \text{Distance from wall}^2 + \text{Height on the wall}^2$ $300^2 = 50^2 + h_1^2$ $90000 = 2500 + h_1^2$ $h_1^2 = 90000 - 2500 = 87500$ $h_1 = \sqrt{87500} \approx 295.8 \, \text{cm}$

Step 2: Final position

After the ladder slips, the base is now $50 + 70 = 120$ cm away from the wall. Again, apply the Pythagorean theorem: $300^2 = 120^2 + h_2^2$ $90000 = 14400 + h_2^2$ $h_2^2 = 90000 - 14400 = 75600$ $h_2 = \sqrt{75600} \approx 274.9 \, \text{cm}$

Step 3: Calculate the slip

The ladder slipped down by: $\text{Slip distance} = h_1 - h_2 = 295.8 - 274.9 = 20.9 \, \text{cm}$

Final Answer:

The ladder slipped 21 cm down the wall.

Would you like a detailed explanation of any step?

5 Related Questions:

1. How does the Pythagorean theorem apply to similar problems involving inclined objects?
2. What would the answer be if the ladder's length were longer or shorter?
3. How does increasing the base's movement affect the height decrease?
4. Can this method be generalized for any type of triangle?
5. Why is it important to measure accurately in real-life applications of this scenario?

Tip:

When using the Pythagorean theorem, ensure all units are consistent (e.g., centimeters or meters).