A right triangle has legs of lengths 8 and 15. What is the length of the hypotenuse?
["# Finding the Hypotenuse: A Right Triangle with Legs 8 and 15", "Understanding how to calculate the hypotenuse of a right triangle is a foundational concept in geometry. Whether you're solving math problems, working on home projects, or just curious about right triangles, knowing how to apply the Pythagorean Theorem makes everything clearer.", "In this article, we’ll explore a classic example: a right triangle with leg lengths 8 and 15. We’ll walk through how to find the length of the hypotenuse step by step.", "## What is the Pythagorean Theorem?", "The Pythagorean Theorem states that in any right 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 (called legs). The formula is:", "[\nc^2 = a^2 + b^2\n]", "Where:\n- ( c ) = length of the hypotenuse\n- ( a ) and ( b ) = lengths of the legs", "---", "## Applying the Theorem to Our Triangle", "Here, the legs are given as:", "- ( a = 8 )\n- ( b = 15 )", "We calculate each squared value:", "[\na^2 = 8^2 = 64\n]\n[\nb^2 = 15^2 = 225\n]", "Add the squares:", "[\nc^2 = 64 + 225 = 289\n]", "Now, take the square root of both sides to find ( c ):", "[\nc = \sqrt{289} = 17\n]", "---", "## Conclusion: The Hypotenuse Measures 17", "Therefore, the length of the hypotenuse in a right triangle with legs 8 and 15 is 17 units.", "---", "### Why This Matters", "Whether you're designing a structure, calculating distances in geometry, or studying for exams, mastering the Pythagorean Theorem is essential. This example with legs 8 and 15 clearly shows how simple math can solve real-world problems involving right angles and distances.", "If you're looking to reinforce your geometry skills, practicing problems like this helps build confidence and a deeper understanding of triangle relationships. Try calculating the hypotenuse for other leg pairs—you’ll find it’s both satisfying and practical!", "---", "Key takeaway: For a right triangle with legs 8 and 15, the hypotenuse is exactly 17. Use the Pythagorean Theorem ( c = \sqrt{a^2 + b^2} ) to find it every time."]
