A right triangle has one leg measuring 9 cm and a hypotenuse measuring 15 cm. What is the length of the other leg?
["How to Find the Missing Leg of a Right Triangle (9 cm & 15 cm Hypotenuse)", "When dealing with right triangles, one of the most essential concepts is the Pythagorean Theorem. This powerful formula relates the three sides of a right triangle and is especially useful when you know two of the side lengths and need to find the missing one.", "### The Problem:\nYou’re given a right triangle where:\n- One leg (let’s call it a) = 9 cm\n- Hypotenuse (c) = 15 cm\n- The other leg (b) is unknown", "We’ll use the Pythagorean Theorem to solve for the missing leg.", "### What is the Pythagorean Theorem?\nThe theorem states:\n[\na^2 + b^2 = c^2\n]\nWhere:\n- a and b are the legs\n- c is the hypotenuse (the side opposite the right angle, and the longest side)", "### Step-by-Step Solution:", "1. Plug in the known values:\n We know a = 9 cm and c = 15 cm.\n [\n 9^2 + b^2 = 15^2\n ]", "2. Calculate the squares:\n [\n 81 + b^2 = 225\n ]", "3. Isolate b²:\n Subtract 81 from both sides:\n [\n b^2 = 225 - 81 = 144\n ]", "4. Solve for b:\n Take the square root of both sides:\n [\n b = \sqrt{144} = 12\n ]", "### ✅ Final Answer:\nThe length of the missing leg is 12 cm.", "This result confirms the triangle follows the Pythagorean relationship:\n[\n9^2 + 12^2 = 81 + 144 = 225 = 15^2\n]\nWhich verifies the solution is correct.", "### Why This Matters:\nUnderstanding how to find missing sides in right triangles is crucial in fields like architecture, engineering, and navigation. With just two sides known, you can quickly determine the third using the Pythagorean Theorem — a skill every student and professional should master.", "Keywords: right triangle, Pythagorean Theorem, missing leg, 9 cm leg, 15 cm hypotenuse, solve right triangle, geometry, math tutorial, 12 cm leg, triangle side calculation."]
