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:
\[ c^2 = a^2 + b^2 \]
where \(c\) is the length of the ladder, \(a\) is the height (48 feet), and \(b\) is the distance from the wall (20 feet).
Plugging the values into the formula:
\[ c^2 = 48^2 + 20^2 \]
Calculating \(48^2\) and \(20^2\):
\[ 48^2 = 2304 \] \[ 20^2 = 400 \]
Now, add those two values:
\[ c^2 = 2304 + 400 = 2704 \]
To find \(c\), take the square root:
\[ c = \sqrt{2704} = 52 \]
So, the length of the ladder is 52 feet.
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