A ladder is leaning against a building, 48 feet going up and 20 feet longways

how long is the ladder

1 answer

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.