Pythagorean Calculator

Pythagorean Theorem Calculator

function calculateHypotenuse() { var sideA = parseFloat(document.getElementById('sideA').value); var sideB = parseFloat(document.getElementById('sideB').value); var resultDiv = document.getElementById('resultHypotenuse'); 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(Math.pow(sideA, 2) + Math.pow(sideB, 2)); resultDiv.innerHTML = 'The Hypotenuse (Side C) Length is: ' + hypotenuse.toFixed(4) + ''; }

Understanding the Pythagorean Theorem

The Pythagorean Theorem is a fundamental principle in geometry that describes the relationship between the three sides of a right-angled triangle. A right-angled triangle is a triangle in which one of the angles is exactly 90 degrees.

The Formula

The theorem states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (called legs). This can be expressed with the following formula:

a² + b² = c²

Where:

• a and b are the lengths of the two shorter sides (legs) of the right triangle.
• c is the length of the hypotenuse, which is always the longest side.

How to Use This Calculator

This Pythagorean Theorem Calculator simplifies the process of finding the length of the hypotenuse (c) when you know the lengths of the two legs (a and b). Simply follow these steps:

1. Enter Side A Length: Input the length of the first leg of your right triangle into the "Side A Length" field.
2. Enter Side B Length: Input the length of the second leg into the "Side B Length" field.
3. Click "Calculate Hypotenuse": The calculator will instantly compute and display the length of the hypotenuse (Side C) based on the Pythagorean formula.

Practical Examples

The Pythagorean Theorem has countless applications in various fields, from construction and engineering to navigation and art. Here are a few examples:

• Example 1: Finding a Diagonal Distance
  Imagine you have a rectangular garden that is 3 meters wide (Side A) and 4 meters long (Side B). To find the diagonal distance across the garden (the hypotenuse), you would calculate:
  3² + 4² = c²
9 + 16 = c²
25 = c²
c = √25 = 5 meters
  Using the calculator with Side A = 3 and Side B = 4 will give you 5.0000.
• Example 2: Ladder Against a Wall
  A ladder is placed against a wall. The base of the ladder is 5 feet away from the wall (Side A), and the wall reaches a height of 12 feet (Side B). To find the length of the ladder (hypotenuse):
  5² + 12² = c²
25 + 144 = c²
169 = c²
c = √169 = 13 feet
  Inputting Side A = 5 and Side B = 12 into the calculator will yield 13.0000.

This calculator is a handy tool for students, educators, and professionals who frequently work with right-angled triangles and need quick, accurate calculations.