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

Question

how long is the ladder

Answer 1

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.