How to Calculate Hypotenuse

Hypotenuse Calculator

Use this calculator to find the length of the hypotenuse of a right-angled triangle using the Pythagorean theorem.

function calculateHypotenuse() { var sideAStr = document.getElementById('sideA').value; var sideBStr = document.getElementById('sideB').value; var resultDiv = document.getElementById('hypotenuseResult'); var sideA = parseFloat(sideAStr); var sideB = parseFloat(sideBStr); if (isNaN(sideA) || isNaN(sideB) || sideA <= 0 || sideB <= 0) { resultDiv.innerHTML = 'Please enter valid positive numbers for both Side A and Side B.'; return; } var hypotenuse = Math.sqrt(sideA * sideA + sideB * sideB); resultDiv.innerHTML = '

Result:

The length of the hypotenuse (Side C) is: ' + hypotenuse.toFixed(4) + ''; }

Understanding the Hypotenuse and the Pythagorean Theorem

In geometry, a right-angled triangle is a triangle in which one of the angles is exactly 90 degrees. The side opposite the right angle is always the longest side and is known as the hypotenuse. The other two sides are called the legs or cathetus.

The Pythagorean Theorem

The relationship between the lengths of the sides of a right-angled triangle is described by the famous Pythagorean Theorem. This theorem states that the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Mathematically, it is expressed as:

a² + b² = c²

Where:

• a is the length of one leg of the right triangle.
• b is the length of the other leg of the right triangle.
• c is the length of the hypotenuse.

To find the length of the hypotenuse (c), you can rearrange the formula to:

c = √(a² + b²)

How to Use This Calculator

Our Hypotenuse Calculator simplifies this process for you. Simply enter the lengths of the two shorter sides (Side A and Side B) of your right-angled triangle into the respective fields. Click the "Calculate Hypotenuse" button, and the calculator will instantly display the length of the hypotenuse (Side C).

Examples of Hypotenuse Calculation

Let's look at a couple of practical examples:

Example 1: A Common Right Triangle

Suppose you have a right-angled triangle where:

• Side A = 3 units
• Side B = 4 units

Using the formula:

c = √(3² + 4²)

c = √(9 + 16)

c = √25

c = 5 units

When you input 3 for Side A and 4 for Side B into the calculator, it will correctly output 5.

Example 2: Another Scenario

Consider a right-angled triangle with:

• Side A = 5 units
• Side B = 12 units

Applying the theorem:

c = √(5² + 12²)

c = √(25 + 144)

c = √169

c = 13 units

The calculator will confirm this result when you enter these values.

Applications of the Hypotenuse and Pythagorean Theorem

The Pythagorean Theorem and the concept of the hypotenuse are fundamental in many fields:

• Construction and Architecture: Used to ensure square corners, calculate roof pitches, and determine diagonal measurements.
• Navigation: Essential for calculating distances between two points on a map or determining a ship's or aircraft's position.
• Engineering: Applied in various engineering disciplines for design and structural analysis.
• Computer Graphics: Used extensively in 2D and 3D graphics for distance calculations and transformations.
• Physics: Fundamental in vector addition and understanding forces and motion.

This calculator provides a quick and accurate way to solve for the hypotenuse, making these calculations straightforward for students, professionals, and anyone needing to work with right-angled triangles.