How to Calculate Hypotenuse

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Hypotenuse Calculator

Calculate the longest side of a right-angled triangle using the Pythagorean Theorem

Result:

Understanding How to Calculate the Hypotenuse

In geometry, the hypotenuse is the longest side of a right-angled triangle. It is always the side directly opposite the 90-degree right angle. Finding the length of the hypotenuse is a fundamental skill in mathematics, physics, and various engineering fields.

The Pythagorean Theorem

The standard method to calculate the hypotenuse is using the Pythagorean Theorem, which states that in a right-angled triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).

a² + b² = c²

Step-by-Step Calculation Guide

  1. Identify the sides: Ensure you are working with a right-angled triangle. Label the two shorter sides as 'a' and 'b'.
  2. Square the sides: Multiply 'a' by itself (a × a) and 'b' by itself (b × b).
  3. Add the squares: Sum the two results together (a² + b²).
  4. Find the square root: Calculate the square root of that sum to find 'c' (the hypotenuse).

Practical Example

Let's say you have a triangle where Side A = 5 cm and Side B = 12 cm.

  • Step 1: 5² = 25
  • Step 2: 12² = 144
  • Step 3: 25 + 144 = 169
  • Step 4: √169 = 13

The hypotenuse length is 13 cm.

Real-World Applications

Calculating the hypotenuse isn't just for school; it's used in:

  • Construction: Ensuring walls are perfectly square.
  • Navigation: Finding the shortest distance between two points on a map.
  • TV Sizes: Television screens are measured diagonally, which is the hypotenuse of the screen's width and height.
  • Architecture: Designing roof pitches and structural supports.
function calculateHypotenuse() { var a = parseFloat(document.getElementById('sideA').value); var b = parseFloat(document.getElementById('sideB').value); var resultBox = document.getElementById('result-box'); var resultValue = document.getElementById('resultValue'); var calculationSteps = document.getElementById('calculationSteps'); if (isNaN(a) || isNaN(b) || a <= 0 || b <= 0) { alert("Please enter valid positive numbers for both sides."); resultBox.style.display = "none"; return; } var aSquared = Math.pow(a, 2); var bSquared = Math.pow(b, 2); var sumOfSquares = aSquared + bSquared; var c = Math.sqrt(sumOfSquares); // Display Logic resultBox.style.display = "block"; // Show math steps for SEO/User value calculationSteps.innerHTML = "Steps: √(" + a + "² + " + b + "²) → √(" + aSquared.toFixed(2) + " + " + bSquared.toFixed(2) + ") → √" + sumOfSquares.toFixed(2); // Show final result rounded to 4 decimal places var finalResult = Number.isInteger(c) ? c : c.toFixed(4); resultValue.innerHTML = "Hypotenuse (c) = " + finalResult; }

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