1. **State the problem:** A ladder 8 m long is leaning against a building. The bottom of the ladder is 3 m from the building. We need to find how high the ladder reaches on the building. 2. **Formula used:** This is a right triangle problem where the ladder is the hypotenuse, the distance from the building is one leg, and the height reached on the building is the other leg. We use the Pythagorean theorem: $$a^2 + b^2 = c^2$$ where $c$ is the hypotenuse (ladder length), $a$ is the distance from the building, and $b$ is the height on the building. 3. **Apply the values:** $$3^2 + b^2 = 8^2$$ 4. **Calculate:** $$9 + b^2 = 64$$ 5. **Isolate $b^2$:** $$b^2 = 64 - 9 = 55$$ 6. **Find $b$ by taking the square root:** $$b = \sqrt{55} \approx 7.42$$ 7. **Answer:** The ladder reaches approximately 7.42 meters high on the building.