Let the triangle have legs \(a = 6\) cm, hypotenuse \(c = 10\) cm. Use the Pythagorean theorem to find the other leg \(b\):
["Understanding Right Triangles: Solving for Leg (b) Using the Pythagorean Theorem", "When dealing with right-angled triangles, one of the most essential tools is the Pythagorean Theorem. This fundamental principle helps determine unknown side lengths when two legs and the hypotenuse are known. In this article, we’ll solve a practical geometry problem involving a right triangle with legs (a = 6) cm and hypotenuse (c = 10) cm—finding the missing leg (b).", "---", "### The Pythagorean Theorem: A Quick Recap", "The Pythagorean Theorem states:", "[\na^2 + b^2 = c^2\n]", "where:\n- (a) and (b) are the legs of the right triangle,\n- (c) is the hypotenuse (the side opposite the right angle).", "This equation allows you to find the unknown leg when the other leg and the hypotenuse are known—exactly our case here.", "---", "### Given Values", "- Leg (a = 6) cm\n- Hypotenuse (c = 10) cm\n- Unknown leg (b) (to be calculated)", "---", "### Step-by-Step Calculation", "Start by substituting the known values into the Pythagorean formula:", "[\n6^2 + b^2 = 10^2\n]", "Calculate the squares:", "[\n36 + b^2 = 100\n]", "Now, isolate (b^2) by subtracting 36 from both sides:", "[\nb^2 = 100 - 36 = 64\n]", "Take the square root of both sides to solve for (b):", "[\nb = \sqrt{64} = 8\n]", "---", "### Result", "The missing leg (b) measures 8 cm. Thus, in a right triangle with legs (a = 6) cm and (b = 8) cm, and hypotenuse (c = 10) cm—this classic triple confirms the relationship:", "[\n6^2 + 8^2 = 10^2 \quad \Rightarrow \quad 36 + 64 = 100\n]", "---", "### Why This Matters", "Understanding how to apply the Pythagorean Theorem expands your ability to solve real-world geometry problems, from construction and navigation to architecture and design. Whether you’re calculating distances, verifying angles, or working with digital graphics, mastering this principle builds a strong foundation in spatial reasoning.", "---", "Keywords: Pythagorean theorem, right triangle, solve for leg b, triangle legs a, triangle hypotenuse c, solve for b in triangle, geometry problem, triangle formulas, 6 cm leg, 10 cm hypotenuse, 8 cm leg, triangle calculations", "Meta Description:\nLearn how to find the missing leg (b) in a right triangle with (a = 6) cm and (c = 10) cm using the Pythagorean theorem. Step-by-step solution and explanation for students and geometry enthusiasts.", "---", "Give your geometry skills a powerful boost—use the Pythagorean Theorem to confidently solve triangle problems today!"]
