c = \sqrt{a^2 + b^2} = \sqrt{15^2 + 20^2} = \sqrt{225 + 400} = \sqrt{625} = 25

["Understanding the Pythagorean Theorem: How to Calculate the Hypotenuse (c = √(a² + b²))", "The Pythagorean theorem is one of the most fundamental principles in geometry, widely used in math, engineering, architecture, and navigation. It provides a simple yet powerful way to calculate the length of the hypotenuse in a right triangle. Whether you're solving a textbook problem or tackling real-world measurements, knowing how to apply the formula correctly is essential.", "## What Is the Pythagorean Theorem?", "The Pythagorean theorem states that in any right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This relationship is expressed mathematically as:", "$$\nc = \sqrt{a^2 + b^2}\n$$", "Here:\n- $ c $ represents the length of the hypotenuse\n- $ a $ and $ b $ are the lengths of the triangle’s two legs (the perpendicular sides)", "## Step-by-Step Example: Calculating the Hypotenuse", "Let’s walk through a classic example using actual numbers:", "Suppose you have a right triangle with legs measuring $ a = 15 $ and $ b = 20 $. To find the hypotenuse $ c $, follow these steps:", "1. Square each leg:\n $$\n a^2 = 15^2 = 225\n $$\n $$\n b^2 = 20^2 = 400\n $$", "2. Add the squares:\n $$\n 225 + 400 = 625\n $$", "3. Take the square root:\n $$\n c = \sqrt{625} = 25\n $$", "So, the length of the hypotenuse is 25 units.", "## Why This Formula Matters", "The ability to compute the hypotenuse using the Pythagorean theorem is crucial in many practical applications:", "- Construction & Carpentry: Ensuring walls and roofs are built at right angles.\n- Navigation & GPS: Calculating shortest distances between points.\n- Physics: Resolving forces and motion vectors.\n- Computer Graphics: Generating accurate shapes and movements.", "## A Quick Recap of the Calculation", "Using the Pythagorean formula:", "$$\nc = \sqrt{a^2 + b^2} = \sqrt{15^2 + 20^2} = \sqrt{225 + 400} = \sqrt{625} = 25\n$$", "This simple calculation demonstrates the elegance and utility of one of geometry’s oldest theorems. Whether you're a student, a professional, or just someone who enjoys mathematical clarity, mastering $ c = \sqrt{a^2 + b^2} $ opens the door to solving countless spatial problems with confidence.", "---", "Key Takeaways:\n- The hypotenuse $ c $ is found using $ \sqrt{a^2 + b^2} $.\n- Practicing basic squaring and square root operations strengthens foundational math skills.\n- The 3-4-5 and 15-20-25 triangles are classic examples that validate the theorem.", "By understanding and applying the Pythagorean theorem, you equip yourself with a timeless tool for geometry and beyond."]