A ladder leans against a wall, forming a right triangle with the ground. The ladder is 13 feet long and the base is 5 feet from the wall. How high up the wall does the ladder reach?
["How High Does a 13-Foot Ladder Reach When Leaned Against a Wall?", "Ladder safety and math go hand in hand when you're trying to figure out how high a ladder reaches up a wall. Whether for homeowners, contractors, or DIY enthusiasts, understanding the right triangle formed by a ladder leaning against a wall is essential—and surprisingly simple with basic geometry.", "### The Right Triangle Basics", "When a ladder leans against a wall, it forms a right triangle where:", "- The ladder is the hypotenuse (13 feet in this case),\n- The distance from the wall base is one leg (5 feet),\n- The height the ladder reaches up the wall is the other leg, which we need to calculate.", "Using the Pythagorean Theorem, this relationship is defined as:", "[\na^2 + b^2 = c^2\n]", "Where:\n- (a) and (b) are the legs (base and height),\n- (c) is the hypotenuse (ladder length).", "---", "### Step-by-Step Calculation", "Given:\n- Ladder length ((c)) = 13 feet\n- Distance from wall ((a)) = 5 feet\n- Height on wall ((b)) = ?", "Plug values into the formula:", "[\n5^2 + b^2 = 13^2\n]", "[\n25 + b^2 = 169\n]", "Subtract 25 from both sides:", "[\nb^2 = 144\n]", "Take the square root:", "[\nb = \sqrt{144} = 12\n]", "---", "### Conclusion", "The ladder reaches 12 feet high up the wall.", "This classic right triangle example helps visualize how distance and height are connected when using a ladder. Always remember: safety starts with accurate measurements, and math ensures you climb smart, not risk.", "Stay safe, leverage geometry, and climb with confidence!", "---", "Keywords: ladder height formula, right triangle ladder, 13 foot ladder height, ladder safety math, Pythagorean theorem ladder, how high a ladder reaches, wall ladder calculation", "Meta Description: Use the Pythagorean theorem to find how high a 13-foot ladder climbs when leaning 5 feet from the wall. Learn step-by-step and ensure safe climbing every time."]
