Use Pythagorean theorem: \(5^2 + h^2 = 13^2\).

["Use the Pythagorean Theorem: Solve for ( h ) in (5^2 + h^2 = 13^2)", "Ever wondered how to find an unknown side in a right triangle? The Pythagorean theorem is your essential tool—especially when dealing with triangles where one angle is exactly 90 degrees. In this article, we’ll walk through how to use the theorem to solve for an unknown leg, using the equation:", "[ 5^2 + h^2 = 13^2 ]", "### 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:", "[ a^2 + b^2 = c^2 ]", "Here, (c) is the hypotenuse, while (a) and (b) are the legs. In our case, (c = 13) (the hypotenuse), (a = 5) (one leg), and (h) is the unknown leg.", "### Step-by-Step Solution", "Start with the equation:", "[\n5^2 + h^2 = 13^2\n]", "First, compute the squares:", "[\n25 + h^2 = 169\n]", "Next, isolate (h^2) by subtracting 25 from both sides:", "[\nh^2 = 169 - 25\n]\n[\nh^2 = 144\n]", "Now, take the square root of both sides to solve for (h):", "[\nh = \sqrt{144} = 12\n]", "### Conclusion", "Using the Pythagorean theorem, we find that if a right triangle has a leg of 5 units and a hypotenuse of 13 units, then the missing leg (h) measures 12 units. This technique is widely applicable in geometry, construction, physics, and navigation—making the Pythagorean theorem a powerful tool for problem-solving.", "Whether you’re calculating distances, designing structures, or solving academic problems, mastering this basic setup:", "[ 5^2 + h^2 = 13^2 ]\n[\Rightarrow h = 12]", "is a fundamental step toward mastering geometry and spatial reasoning.", "Keywords: Pythagorean theorem, how to use the Pythagorean theorem, solve right triangles, use Pythagoras, find missing side, 5² + h² = 13², mathematics practice, geometry problem-solving, algebra application."]