A ladder 13 meters long leans against a vertical wall. If the foot of the ladder is 5 meters from the wall, how high up the wall does the ladder reach?

Sun, 03 May 2026 14:41:50 +0000

**How a 13-Meter Ladder Reaches a Wall: The Mathematics Behind Safety and Limits** Have you ever stood before a sturdy ladder leaning against a vertical wall—13 meters long—and wondered just how high it climbs when planted firmly 5 meters from its base? With home improvement projects, rental inspections, and DIY safety guiding everyday conversations across the U.S., this question isn’t just academic—it’s practical. As Americans tackle roof maintenance, grassroots construction, or rental property checks, understanding how ladders interact with walls becomes essential for safety and confidence. This guide breaks down the physics, math, and real-world meaning behind the ladder formula—so you know exactly how high a 13-meter ladder climbs when placed 5 meters from the wall. **The Science Behind a Ladder Approaching a Wall** A 13-meter ladder leaning at a perfect 75-degree angle against a vertical wall forms a classic triangle physics problem. When the ladder’s base stands 5 meters from the wall, the height it reaches combines geometry with stability principles. Using the Pythagorean theorem, we calculate the wall height based on a 90-degree right angle where wall, floor, and ladder meet. For a ladder fixed rigidly at one end (on the ground), its full length acts as the hypotenuse, and the wall height determines the opposite side in a right triangle. The equation remains consistent regardless of unit preference: