A ladder 10 feet long leans against a wall, reaching 8 feet up. How far is the base from the wall?
["A 10-Foot Ladder Leaning Against a Wall — How Far Does the Base Sit From the Wall?", "When a 10-foot ladder leans against a wall, a classic geometry problem unfolds: how far should the base be from the wall to ensure stability? Not only is this a common scenario in homes, construction, and DIY projects, but it also offers a practical application of the Pythagorean theorem. If the ladder reaches 8 feet up the wall, you may wonder: how far is the ladder’s base from the wall? Let’s break down the math and the physics behind this question.", "### Understanding the Geometry", "Imagine the ladder as the hypotenuse of a right triangle:", "- The ladder is the hypotenuse: 10 feet\n- The height it reaches on the wall is one leg: 8 feet\n- The distance from the wall to the base of the ladder is the other leg: what we want to find (call it x)", "Using the Pythagorean theorem:\n[\na^2 + b^2 = c^2\n]\nwhere\n- ( a = x ) (distance from wall),\n- ( b = 8 ) feet (height up wall),\n- ( c = 10 ) feet (ladder length).", "Plugging in the values:\n[\nx^2 + 8^2 = 10^2\n]\n[\nx^2 + 64 = 100\n]\n[\nx^2 = 100 - 64 = 36\n]\n[\nx = \sqrt{36} = 6\n]", "### Answer: The Base Is 6 Feet from the Wall", "So, the base of the ladder should be 6 feet away from the wall to safely support the 8-foot climb on an 18-foot (10-foot) ladder.", "### Why Distance Matters", "Placing the ladder too close to the wall risks instability — a higher foot position increases leverage, making the ladder prone to slipping. Conversely, moving the base too far reduces effective reach. A safe distance minimizes risk and maximizes efficiency.", "### Additional Safety Tips", "- Always extend the base 1 to 3 feet beyond the foot of the ladder for extra grip and stability.\n- Ensure the ladder rests on a stable, level surface.\n- Avoid overreaching — stay within the recommended reach.\n- In high-risk situations, use ladder stabilizers or rent a stepladder.", "### Summary", "For a 10-foot ladder reaching 8 feet up a wall:\nThe base is 6 feet from the wall.\nThis calculation combines simple geometry with real-world safety, proving that even a simple ladder setup benefits from a clear mathematical foundation.", "Next time you grab a ladder, remember: 10-foot ladder, 8 feet high → 6 feet base distance. It’s a small measure that ensures safety and success."]
