To find the length of the ladder, we can use the Pythagorean theorem. The ladder forms a right triangle with the wall and the ground, where:
- One leg is the height up the wall (48 feet),
- The other leg is the distance from the bottom of the ladder to the wall (20 feet),
- The hypotenuse is the length of the ladder (which we want to find).
According to the Pythagorean theorem:
where
Plugging the values into the formula:
Calculating
Now, add those two values:
To find
So, the length of the ladder is 52 feet.