The base of a 6.0-m ladder is 1.8 m from a wall. To find how far up on the wall the ladder reaches, we can use the Pythagorean theorem, which states that for a right triangle with legs of lengths

$$a$$ and

$$b$$ and hypotenuse of length

$$c$$ The following equation holds:

$$a^2+b^2=c^2$$

In this case, the ladder is the hypotenuse, so we can let

$$c=6.0\text{ m}$$ The distance from the base of the ladder to the wall is

$$a=1.8\text{ m}$$ We can solve for the length of the ladder up the wall (b),

$$b^2=c^2-a^2$$

$$b^2=(6.0\text{ m}{)}^2-(1.8\text{ m}{)}^2$$

$$b^2=36m-3.24m$$

$$b^2=32.76{\text{ m}}^2$$

$$b=\sqrt{32.76{\text{ m}}^2}$$

$$b\approx 5.72\text{ m}$$

Therefore, the ladder reaches up about

$$5.72\text{ m on the wall.}$$