A ladder is leaning against a wall, forming a right triangle with the ground. If the ladder is 13 feet long and the base is 5 feet from the wall, how high does the ladder reach on the wall?

Tue, 05 May 2026 22:12:32 +0000

**A ladder is leaning against a wall, forming a right triangle with the ground. If the ladder is 13 feet long and the base is 5 feet from the wall, how high does the ladder reach on the wall?** Curious about the simple geometry behind a common scene—this right triangle isn’t just a math problem. It’s something most U.S. homeowners, renters, and DIY enthusiasts run into daily. Whether installing shelves, reaching a high shelf, or simply understanding scale and structure, knowing how height relates to distance is essential. When a 13-foot ladder leans against a wall with its base 5 feet from the wall, the right triangle formed allows us to apply basic trigonometry. The ladder acts as the hypotenuse (13 feet), the base distance is one leg (5 feet), and the wall height is the other leg—what we’re calculating. Using the Pythagorean Theorem, the height reaches approximately 12.08 feet. This height helps set realistic expectations for storage, climbing safety, and space use. **Why This Right Triangle Math Is Gaining Attention in the U.S.**