1. **Problem statement:** We have a right triangle formed by a lamp of height 3 m, a building of height $H$ meters, and the horizontal distance between them is 20 m. We need to find the height $H$ of the building. 2. **Understanding the triangle:** The lamp height is 3 m, and the horizontal distance from the lamp to the building is 20 m. The hypotenuse is the line from the top of the lamp to the top of the building. 3. **Using the Pythagorean theorem:** For a right triangle with legs $a$ and $b$, and hypotenuse $c$, the relation is: $$a^2 + b^2 = c^2$$ 4. **Assigning values:** Let the vertical side of the building be $H$, the vertical side of the lamp be 3 m, and the horizontal distance between the lamp and building be 20 m. 5. **Calculate the vertical difference:** The vertical difference between the top of the building and the lamp is $H - 3$. 6. **Apply Pythagoras:** The hypotenuse is the distance from the lamp top to the building top, which is the straight line connecting these points. The horizontal leg is 20 m, and the vertical leg is $H - 3$. So, $$20^2 + (H - 3)^2 = \text{hypotenuse}^2$$ But since the hypotenuse is not given, we need more information or a missing angle or length to solve for $H$. Since the problem does not provide the hypotenuse or angle, we assume the hypotenuse is the line from lamp top to building top. 7. **Re-examining the problem:** The problem states the lamp is 20 m from the building, and the lamp height is 3 m. The triangle formed has base 20 m, height $H - 3$, and hypotenuse unknown. If the hypotenuse length is not given, we cannot solve for $H$ directly. Possibly the problem expects $H$ to be calculated assuming the hypotenuse is the line from lamp top to building top. 8. **Conclusion:** Without additional data (such as the length of the hypotenuse or an angle), the height $H$ cannot be determined uniquely. **Final answer:** Insufficient information to calculate $H$.