1. **State the problem:** A 6-m extension ladder leans against a vertical wall with its base 2 m from the wall. We need to find how high up the wall the top of the ladder reaches. 2. **Formula used:** This is a right triangle problem where the ladder is the hypotenuse, the distance from the wall is one leg, and the height up the wall is the other leg. We use the Pythagorean theorem: $$h = \sqrt{l^2 - b^2}$$ where $h$ is the height up the wall, $l$ is the length of the ladder (hypotenuse), and $b$ is the base distance from the wall. 3. **Substitute the known values:** $$h = \sqrt{6^2 - 2^2}$$ 4. **Calculate the squares:** $$h = \sqrt{36 - 4}$$ 5. **Simplify inside the square root:** $$h = \sqrt{32}$$ 6. **Calculate the square root:** $$h = 5.656854249$$ 7. **Round to the nearest tenth:** $$h \approx 5.7$$ meters **Final answer:** The top of the ladder reaches approximately 5.7 meters up the wall.