Solution: Let the legs of the right triangle be $ a = 15 $ km and $ b = 20 $ km. The hypotenuse $ c $ is given by the Pythagorean theorem:
["Finding the Hypotenuse of a Right Triangle: A Practical Solution Using the Pythagorean Theorem", "When working with right triangles, one of the most essential calculations is determining the length of the hypotenuse when the two legs are known. This concept is widely used in fields such as architecture, engineering, navigation, and everyday problem-solving. In this article, we’ll explore a clear, step-by-step solution to a classic right triangle problem: finding the hypotenuse when the legs measure $ a = 15 $ km and $ b = 20 $ km.", "---", "### The Classic Right Triangle Setup", "Consider a right triangle with perpendicular legs $ a $ and $ b $, and hypotenuse $ c $. According to the Pythagorean theorem, the relationship is:", "$$\nc = \sqrt{a^2 + b^2}\n$$", "Here, $ a = 15 $ km and $ b = 20 $ km.", "---", "### Step-by-Step Calculation", "1. Square the leg lengths:\n $ a^2 = 15^2 = 225 $\n $ b^2 = 20^2 = 400 $", "2. Add the squares:\n $ a^2 + b^2 = 225 + 400 = 625 $", "3. Take the square root:\n $ c = \sqrt{625} = 25 $", "---", "### Final Result", "The hypotenuse $ c $ measures 25 km.", "Thus, the right triangle with legs 15 km and 20 km has a hypotenuse of exactly 25 km — a perfect example of the Pythagorean triple (15, 20, 25), which is a multiple of the well-known 3-4-5 triangle.", "---", "### Why This Matters", "Understanding hypotenuse calculation strengthens your ability to:", "- Solve real-world distance problems (e.g., diagonal path lengths, ladder placements)\n- Verify right angles in construction or design projects\n- Build a foundation for more advanced geometry and trigonometry", "Whether you're geeks, students, or professionals, mastering the Pythagorean theorem opens doors to practical applications every day.", "---", "### Pro Tip", "Never forget the formula:\n$$\nc = \sqrt{a^2 + b^2}\n$$\nIt’s fast, reliable, and essential for working with right triangles.", "---", "Keywords: hypotenuse calculation, right triangle, Pythagorean theorem, solve triangle, a=15 km, b=20 km, find hypotenuse, Pythagorean triple, geometry practice.\nMeta Description: Learn how to calculate the hypotenuse of a right triangle with legs 15 km and 20 km using the Pythagorean theorem. Step-by-step solution + real-world relevance. Perfect for students, engineers, and DIY enthusiasts."]
