A ladder 13 feet long is leaning against a wall. The foot of the ladder is 5 feet from the wall. How high up the wall does the ladder reach?

Mon, 04 May 2026 17:10:40 +0000

**Why Hor viz PDF 13-foot aspiration leaning against a wall. The foot rests 5 feet from the corner—how high does it rise? When not making headlines for controversy, this straightforward physics puzzle keeps surfacing in everyday questions. From home renovations to DIY guidance, people naturally wonder: when a ladder stands firm with one base five feet from the wall, exactly where does it meet the height above ground? The answer lies in simple geometry—and is far more accessible than many assume. **Understanding the Math Behind the Ladder’s Touch**
The common 13-foot ladder leans at a precise 5-foot base distance from the wall, forms a right triangle with the wall, ground, and the ladder itself. Using the Pythagorean theorem—length² = height² + base²—we calculate square root(169 – 25) = √144 = 12. So the top of the ladder reaches 12 feet up the wall. This moment has little to do with trends or tech, but immense relevance in safety, planning, and everyday problem-solving. **Why This Common Scenario Keeps Growing in Relevance**
Across the United States, this type of setup appears frequently in urban and suburban settings: overflowing tool sheds, outdoor projects, rental properties with basic ladders, or temporary housing setups. As more people break into DIY, construction, or even니다房 rental—often on tight budgets—understanding safe working heights becomes essential. The query’s visibility reflects a quiet demand for clear, reliable guidance—not sensational headlines, but actionable knowledge. **How Exactly High Does a 13-Foot Ladder Reach When Set 5 Feet From the Wall?**
To clarify, if a 13-foot ladder rests with its base 5 feet from the wall, the top touches the wall at a height of 12 feet. This follows the well-tested formula from elementary geometry: the square of the ladder’s length minus the square of the base distance equals the square of the wall height. It’s a precise calculation, consistently accurate and taught in home safety materials, trade training, and instructional videos. The result stays the same across locales—4 walls, coast to coast, remains