To repair a roof that is 3 meters high, Mr. Palmer leans a 5-meter ladder against the side of the building. To reach the roof, how far away from the building should he place the base of the ladder?

To solve this, we can use the Pythagorean theorem since the ladder, wall, and ground form a right triangle. In this case:

- The height of the roof (vertical side) is \( a = 3 \) meters.
- The length of the ladder (hypotenuse) is \( c = 5 \) meters.
- We need to find the distance \( b \), the horizontal distance from the base of the ladder to the wall.

The Pythagorean theorem states:
\[
a^2 + b^2 = c^2
\]

Plugging in the known values:
\[
3^2 + b^2 = 5^2
\]
\[
9 + b^2 = 25
\]
Subtracting 9 from both sides:
\[
b^2 = 16
\]
Taking the square root of both sides:
\[
b = 4
\]

Therefore, Mr. Palmer should place the base of the ladder **4 meters away from the building** to reach the roof safely.

Would you like further details on this solution?

Here are five related questions for further exploration:
1. What if the roof height was increased to 4 meters, keeping the ladder length the same?
2. How would the angle of the ladder with the ground change if he moved it further from the building?
3. What if Mr. Palmer used a 6-meter ladder—how far should he place it from the wall?
4. What would happen if the ground was not level? How would that affect ladder placement?
5. How do you calculate the angle at which the ladder meets the ground?

**Tip:** When using a ladder, it's safest if it forms about a 75° angle with the ground for stability.

Learn how to calculate the distance to place a ladder safely from a building. Given a roof height of 3 meters and a ladder length of 5 meters, solve for the base distance using the Pythagorean theorem. Ideal for students in Grades 6-8.

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