In a right triangle, the hypotenuse is 25 cm, and one leg is 7 cm. What is the length of the other leg?
["# Finding the Missing Leg in a Right Triangle: A 25 cm Hypotenuse and One Leg of 7 cm", "When studying right triangles, one of the most fundamental problems is finding the length of a missing leg when the hypotenuse and the other leg are known. In geometry, the Pythagorean Theorem provides the perfect solution for this scenario. In this article, we’ll walk through how to find the missing leg when the hypotenuse is 25 cm and one leg measures 7 cm. Whether you're a student learning geometry or simply curious about triangle calculations, this guide will help you master the process step by step.", "## The Pythagorean Theorem: A Quick Recap", "The Pythagorean Theorem states:\n[\na^2 + b^2 = c^2\n]\nwhere ( c ) represents the hypotenuse (the side opposite the right angle), and ( a ) and ( b ) are the two legs of the triangle. Given values are:\n- Hypotenuse ( c = 25 ) cm\n- One leg ( a = 7 ) cm\n- Missing leg ( b = ? )", "## Applying the Theorem Step-by-Step", "### Step 1: Plug known values into the formula\nStart with the Pythagorean formula and substitute the known lengths:\n[\n7^2 + b^2 = 25^2\n]", "### Step 2: Calculate the squares\n[\n49 + b^2 = 625\n]", "### Step 3: Solve for ( b^2 )\nSubtract 49 from both sides to isolate ( b^2 ):\n[\nb^2 = 625 - 49 = 576\n]", "### Step 4: Take the square root\nNow find ( b ) by taking the square root of 576:\n[\nb = \sqrt{576} = 24\n]", "## Result: The Length of the Missing Leg", "The missing leg measures 24 cm. This means a right triangle with a 25 cm hypotenuse and one leg of 7 cm has the other leg precisely 24 cm long.", "## Real-World Applications", "Understanding how to find missing sides in right triangles is essential in fields like architecture, engineering, navigation, and carpentry. For example, if a builder needs to verify a structural triangle has the correct dimensions, or a student designs a model using Pythagorean principles, knowing how to solve for unknown legs is invaluable.", "## Conclusion", "By applying the Pythagorean Theorem, we efficiently determine that in a right triangle with a hypotenuse of 25 cm and one leg of 7 cm, the length of the other leg is 24 cm. This fundamental relationship underpins countless geometric calculations and real-world applications—making it a cornerstone of safe and accurate spatial reasoning.", "---", "Keywords: right triangle, hypotenuse, leg length, Pythagorean Theorem, 25 cm hypotenuse, missing leg calculation, geometry problem, triangle formulas, math tutorial", "Meta Description: Learn how to find the missing leg in a right triangle using the Pythagorean Theorem. With a hypotenuse of 25 cm and one leg 7 cm, we show step-by-step how the other leg measures 24 cm. Ideal for students and DIY enthusiasts."]
