A ladder 10 meters long leans against a wall. If the base is 6 meters from the wall, how high does the ladder reach?

Mon, 04 May 2026 17:47:50 +0000

**How High Does a 10-Meter Ladder Reach When Its Base Is 6 Meters From the Wall?**
A question crafting curiosity about geometry and everyday safety—this classic wall ladder problem resonates more than you’d expect. With rising interest in home maintenance, DIY trends, and safe household habits, understanding ladder angles isn’t just academic—it’s essential. As Americans seek reliable tips for safe home use, this simple yet precise calculation reveals practical knowledge behind a familiar sight. **Why Ladders Like This Matter in the US**
Recent digital trends show growing awareness around home safety and proper equipment use, especially in DIY and renting communities. The 10-meter ladder is a common length for professional and DIY tasks, whether on construction sites, rooftop repairs, or extended reach tasks. When the base sits 6 meters from the wall, the math behind how high it climbs intersects with real-world safety considerations. With mounting emphasis on responsible home management, this question isn’t just about height—it’s about confidence and informed decisions. **How It All Adds Up: The Math Behind the Climb**
A ladder leaning against a wall follows a basic principle of right-angle geometry. The length of the ladder acts as the hypotenuse—a straight line connecting the base of the wall, top of the ladder, and the point where they meet at a right angle. When the base is 6 meters from the wall, applying the Pythagorean Theorem reveals the precise vertical reach. Using the formula:
**a² + b² = c²**
Where
- c = ladder length = 10 meters
- a = distance from wall (6 meters)
- b = height on the wall (unknown)