We can solve this problem using the Pythagorean theorem.

Initial Setup

The ladder, the house, and the ground form a right triangle.

• The length of the ladder is 50 feet (this is the hypotenuse of the right triangle).
• The initial height the ladder reaches up the house is 48 feet (this is one leg of the triangle).
• The distance from the base of the ladder to the house is the other leg of the triangle. We can find this using the Pythagorean theorem.

Step 1: Find the initial distance from the base of the ladder to the house

We know:

• Hypotenuse $c = 50$ feet
• One leg $a = 48$ feet

Using the Pythagorean theorem: $a^2 + b^2 = c^2$ $48^2 + b^2 = 50^2$ $2304 + b^2 = 2500$ $b^2 = 2500 - 2304 = 196$ $b = \sqrt{196} = 14 \text{ feet}$

So, the initial distance from the base of the ladder to the house is 14 feet.

Step 2: After Mila pulls the ladder 6 feet farther

Now, the distance from the base of the ladder to the house is: $14 + 6 = 20 \text{ feet}$

Step 3: Find the new height the ladder will reach

Now we apply the Pythagorean theorem again, with the new distance of 20 feet as one leg and the ladder's length of 50 feet as the hypotenuse.

$a^2 + 20^2 = 50^2$ $a^2 + 400 = 2500$ $a^2 = 2500 - 400 = 2100$ $a = \sqrt{2100} \approx 45.8 \text{ feet}$

Final Answer:

After Mila pulls the ladder, it will reach approximately 45.8 feet up the side of the house.

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Would you like any further details or explanations? Here are some related questions:

1. How would the height change if the ladder were even longer (e.g., 60 feet)?
2. What if Mila had pulled the ladder 10 feet farther?
3. How would the height change if the ladder were initially set at a greater angle (e.g., 60 degrees)?
4. What is the role of the Pythagorean theorem in real-life situations like this?
5. How could this problem be solved if the ladder was leaning against a tree instead of a house?

Tip: Always visualize the problem as a right triangle, with the ladder as the hypotenuse. It will make it easier to apply the Pythagorean theorem.