A right triangle has legs of lengths 9 cm and 12 cm. What is the length of the hypotenuse?
["Title: How to Calculate the Hypotenuse of a Right Triangle With Legs 9 cm and 12 cm", "Understanding right triangles is fundamental in geometry, especially when calculating unknown side lengths using the Pythagorean Theorem. If you're trying to find the hypotenuse of a right triangle with legs measuring 9 cm and 12 cm, this article guides you step-by-step through the calculation with clear explanations and real-world applications.", "---", "### The Pythagorean Theorem: A Quick Refresher", "For any right triangle, the relationship between the two legs (often called a and b) and the hypotenuse (c) is defined by the Pythagorean Theorem:", "[\nc^2 = a^2 + b^2\n]", "Where:\n- ( a = 9 ) cm\n- ( b = 12 ) cm\n- ( c ) = hypotenuse (what we want to find)", "---", "### Step-by-Step Calculation", "1. Square the lengths of both legs:\n[\na^2 = 9^2 = 81\n]\n[\nb^2 = 12^2 = 144\n]", "2. Add the squares:\n[\nc^2 = 81 + 144 = 225\n]", "3. Take the square root to find c:\n[\nc = \sqrt{225} = 15 \ ext{ cm}\n]", "---", "### Final Answer", "The hypotenuse of a right triangle with legs 9 cm and 12 cm is 15 cm.", "---", "### Why This Matters: Real-World Uses of the Hypotenuse", "Knowing the hypotenuse is crucial in various practical situations, such as:", "- Calculating roof pitches or sloped surfaces in carpentry\n- Designing staircases and diagonal supports\n- Navigating shortest distances between two points\n- Understanding vector components in physics and engineering", "---", "### Summary", "For a right triangle with legs 9 cm and 12 cm:\n- Use ( c = \sqrt{a^2 + b^2} )\n- Compute ( c = \sqrt{81 + 144} = \sqrt{225} = 15 ) cm", "Mastering this simple calculation unlocks more complex geometric and trigonometric concepts critical in both academic and professional fields.", "---", "Keywords: right triangle hypotenuse, Pythagorean Theorem, legs 9 cm and 12 cm, calculate hypotenuse, geometry tutorial, triangle side length, 9 and 12 cm triangle, hypotenuse formula", "Meta Description: Find the hypotenuse of a right triangle with legs measuring 9 cm and 12 cm. Use the Pythagorean Theorem for fast, accurate results—ideal for students and real-world applications."]
