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**),
$$b^2 = c^2 - a^2$$

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

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

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

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

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

Therefore, the ladder reaches up about $$5.72 \text{ m on the wall.}$$