Eine Leiter lehnt an einer Wand und bildet einen Winkel von 60 Grad zum Boden. Wenn die Leiter 10 Meter lang ist, wie hoch reicht sie an der Wand?

Thu, 30 Apr 2026 12:06:09 +0000

## Learn How a 10-Meter Ladder Reaches 8.66 Meters Up a Wall—Without Math Anxiety Curious about how angles and distances interact in everyday setups? A classic geometry question—like “If a 10-meter-long ladder leans at a 60-degree angle against a wall, how high does it reach?”—captures real-world curiosity about physics, space, and safety. This visible problem appears more than just a math puzzle: it resonates with DIY enthusiasts, renters updating homes, and small space dwellers seeking efficient solutions. People searching “Eine Leiter lehnt an einer Wand und bildet einen Winkel von 60 Grad zum Boden. Wenn die Leiter 10 Meter lang ist, wie hoch reicht sie an der Wand?” are often navigating home improvement decisions, evaluating furniture placement, or understanding DIY project limits. This article explains the answer clearly—without fluff—and explores the broader context behind the math. ### The Science Behind the Slope: What the Angle Really Means When a ladder rests at a 60-degree angle against a vertical wall, the geometry hinges on trigonometry, but it’s simpler than it sounds. The ladder forms the hypotenuse of a right triangle, with the wall as one leg and the floor as the base. Using sine—defined as opposite over hypotenuse—makes the calculation direct: sin(60°) = height / 10. Since sin(60°) equals √3/2, the height becomes 10 × √3/2 = 5√3 meters, approximately 8.66 meters. This precise relationship reveals a small household detail with big implications: knowing ladder height helps prevent tip-overs, ensures safe leaning angles, and guides placement in tight spaces.