A ladder 10 meters long leans against a wall, reaching a height of 8 meters. How far is the base of the ladder from the wall?
["How Far is the Base of a 10-Meter Ladder from the Wall When It Reaches 8 Meters High?", "When dealing with basic physics and geometry, ladder problems are a classic example of applying the Pythagorean theorem — especially when a ladder leans against a wall. Suppose you have a ladder that’s 10 meters long, leaning against a wall, and reaching a height of 8 meters. A common question arises: How far is the base of the ladder from the wall?", "This article explains how to solve the problem step by step, why the ladder forms a right triangle, and how to use the Pythagorean theorem to find the distance.", "---", "### The Physics: A Right Triangle in Real Life", "A 10-meter ladder leaning against a wall forms a right triangle:", "- The ladder acts as the hypotenuse — the longest side, opposite the right angle.\n- The height it reaches on the wall is one leg of the triangle (8 meters).\n- The distance from the wall base to the foot of the ladder is the other leg, which we want to find.", "---", "### Applying the Pythagorean Theorem", "The Pythagorean theorem states:", "[\n\ ext{(Hypotenuse)}^2 = \ ext{(Leg 1)}^2 + \ ext{(Leg 2)}^2\n]", "Let:", "- ( c = 10 ) meters (ladder length = hypotenuse)\n- ( a = 8 ) meters (height reached on wall)\n- ( b = ? ) (distance from wall — the unknown base distance)", "Plug into the formula:", "[\n10^2 = 8^2 + b^2\n]", "[\n100 = 64 + b^2\n]", "[\nb^2 = 100 - 64 = 36\n]", "[\nb = \sqrt{36} = 6\n]", "---", "### The Answer: 6 Meters", "The base of the ladder is 6 meters away from the wall.", "---", "### Visual & Practical Insight", "- When a ladder leans at an angle, its height and horizontal distance are balanced by the ladder’s length.\n- This principle applies in construction, home repairs, and physics problems involving forces and stability.\n- Understanding this relationship helps prevent slipping — a key safety tip: keep the base shorter than half the ladder height, ideally ~3–4 meters small than the wall height in similar setups.", "---", "### Want to Learn More?", "Explore related topics:", "- How to calculate ladder angle and stability\n- Real-world applications of the Pythagorean theorem\n- Safety guidelines for ladder placement", "---", "Conclusion:\nA 10-meter ladder reaching 8 meters up a wall is safely positioned 6 meters from the wall — a perfect example of combining geometry with real-world utility. Whether for homework, DIY projects, or physics learning, mastering this simple layout builds confidence in tackling more complex problems.", "---", "Keywords for SEO:\n10-meter ladder height calculation, ladder leaning against wall distance, Pythagorean theorem ladder problem, how far is ladder base from wall, right triangle ladder height, ladder placement safety, 10-meter ladder math, do ladders lean using Pythagoras, ladder height and base distance, 8-meter ladder reach solution"]
