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:

c2=a2+b2

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:

c2=482+202

Calculating 482 and 202:

482=2304 202=400

Now, add those two values:

c2=2304+400=2704

To find c, take the square root:

c=2704=52

So, the length of the ladder is 52 feet.