Pythagoras Theorem Calculation

body {
font-family: ‘Segoe UI’, Tahoma, Geneva, Verdana, sans-serif;
background-color: #f8f9fa;
color: #333;
line-height: 1.6;
margin: 0;
padding: 20px;
display: flex;
flex-direction: column;
align-items: center;
}
.loan-calc-container {
background-color: #ffffff;
padding: 30px;
border-radius: 8px;
box-shadow: 0 4px 15px rgba(0, 0, 0, 0.1);
max-width: 700px;
width: 100%;
margin-bottom: 30px;
}
h1 {
color: #004a99;
text-align: center;
margin-bottom: 25px;
}
.input-group {
margin-bottom: 20px;
display: flex;
align-items: center;
flex-wrap: wrap;
}
.input-group label {
flex: 1 1 150px;
min-width: 120px;
margin-right: 15px;
font-weight: 600;
color: #004a99;
}
.input-group input[type=”number”] {
flex: 2 1 200px;
padding: 10px 15px;
border: 1px solid #ccc;
border-radius: 4px;
font-size: 1rem;
box-sizing: border-box;
}
.input-group input[type=”number”]:focus {
outline: none;
border-color: #004a99;
box-shadow: 0 0 0 2px rgba(0, 74, 153, 0.2);
}
button {
display: block;
width: 100%;
padding: 12px 20px;
background-color: #28a745;
color: white;
border: none;
border-radius: 4px;
font-size: 1.1rem;
cursor: pointer;
transition: background-color 0.3s ease;
margin-top: 10px;
}
button:hover {
background-color: #218838;
}
#result {
margin-top: 25px;
padding: 20px;
background-color: #e7f3ff;
border: 1px solid #cce5ff;
border-radius: 5px;
text-align: center;
font-size: 1.5rem;
font-weight: bold;
color: #004a99;
}
#result span {
font-size: 1.2rem;
font-weight: normal;
color: #333;
}
.article-section {
background-color: #ffffff;
padding: 30px;
border-radius: 8px;
box-shadow: 0 4px 15px rgba(0, 0, 0, 0.1);
max-width: 700px;
width: 100%;
margin-top: 30px;
text-align: left;
}
.article-section h2 {
color: #004a99;
margin-bottom: 15px;
border-bottom: 2px solid #004a99;
padding-bottom: 5px;
}
.article-section p, .article-section ul {
margin-bottom: 15px;
}
.article-section code {
background-color: #e7f0fa;
padding: 2px 5px;
border-radius: 3px;
font-family: ‘Courier New’, Courier, monospace;
}
@media (max-width: 600px) {
.input-group {
flex-direction: column;
align-items: stretch;
}
.input-group label {
margin-right: 0;
margin-bottom: 5px;
}
.input-group input[type=”number”] {
width: 100%;
margin-top: 5px;
}
}

Calculate the length of the hypotenuse (c) or one of the legs (a or b) of a right-angled triangle.

Understanding the Pythagorean Theorem

The Pythagorean theorem is a fundamental principle in Euclidean 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 (a right angle).

The theorem states that the square of the length of the hypotenuse (the side opposite the right angle, usually denoted as ‘c’) is equal to the sum of the squares of the lengths of the other two sides (the legs, usually denoted as ‘a’ and ‘b’).

The Formula

Mathematically, the theorem is expressed as:

a² + b² = c²

• a and b are the lengths of the two legs of the right-angled triangle.
• c is the length of the hypotenuse.

How the Calculator Works

This calculator allows you to find a missing side length of a right-angled triangle:

• If you input values for both a and b, it will calculate c (the hypotenuse).
• If you input a value for c (hypotenuse) and one of the legs (a or b), it will calculate the missing leg.
• If you provide all three values, it will check if they form a valid right-angled triangle.

Use Cases

The Pythagorean theorem has numerous applications in various fields:

• Construction and Architecture: Ensuring that corners are perfectly square (90 degrees), calculating diagonal braces, and determining roof slopes.
• Navigation: Calculating the shortest distance between two points on a flat map or across a body of water.
• Engineering: Used in designing structures, calculating distances, and understanding forces.
• Computer Graphics: Calculating distances between points, collision detection, and rendering.
• Everyday Life: Estimating distances, determining if a surface is level, or even calculating how much material is needed for a diagonal cut.

Example Calculation

Consider a right-angled triangle where side A is 3 units and side B is 4 units. Using the theorem:

a² + b² = c²

3² + 4² = c²

9 + 16 = c²

25 = c²

Taking the square root of both sides:

c = √25

c = 5

So, the hypotenuse is 5 units long.

Alternatively, if the hypotenuse (c) is 13 units and side A is 5 units, we can find side B:

a² + b² = c²

5² + b² = 13²

25 + b² = 169

b² = 169 - 25

b² = 144

b = √144

b = 12

So, side B is 12 units long.

function calculatePythagorean() {
var sideAInput = document.getElementById(“sideA”);
var sideBInput = document.getElementById(“sideB”);
var hypotenuseCInput = document.getElementById(“hypotenuseC”);
var resultDiv = document.getElementById(“result”);

var sideA = parseFloat(sideAInput.value);
var sideB = parseFloat(sideBInput.value);
var hypotenuseC = parseFloat(hypotenuseCInput.value);

var calculationType = “”;
var calculatedValue = NaN;

if (!isNaN(sideA) && !isNaN(sideB) && sideA > 0 && sideB > 0) {
// Calculate hypotenuse C if A and B are provided
calculatedValue = Math.sqrt(sideA * sideA + sideB * sideB);
calculationType = “Hypotenuse (c)”;
resultDiv.innerHTML = “The calculated ” + calculationType + ” is: ” + calculatedValue.toFixed(4) + ““;
sideAInput.value = sideA.toFixed(4);
sideBInput.value = sideB.toFixed(4);
hypotenuseCInput.value = “”; // Clear the hypotenuse input if it was calculated
} else if (!isNaN(hypotenuseC) && !isNaN(sideA) && hypotenuseC > 0 && sideA > 0) {
// Calculate side B if C and A are provided
if (hypotenuseC > sideA) {
calculatedValue = Math.sqrt(hypotenuseC * hypotenuseC – sideA * sideA);
calculationType = “Side B”;
resultDiv.innerHTML = “The calculated ” + calculationType + ” is: ” + calculatedValue.toFixed(4) + ““;
sideAInput.value = sideA.toFixed(4);
hypotenuseCInput.value = hypotenuseC.toFixed(4);
sideBInput.value = “”; // Clear the side B input
} else {
resultDiv.innerHTML = “Error: Hypotenuse (C) must be greater than Side A.“;
return;
}
} else if (!isNaN(hypotenuseC) && !isNaN(sideB) && hypotenuseC > 0 && sideB > 0) {
// Calculate side A if C and B are provided
if (hypotenuseC > sideB) {
calculatedValue = Math.sqrt(hypotenuseC * hypotenuseC – sideB * sideB);
calculationType = “Side A”;
resultDiv.innerHTML = “The calculated ” + calculationType + ” is: ” + calculatedValue.toFixed(4) + ““;
sideBInput.value = sideB.toFixed(4);
hypotenuseCInput.value = hypotenuseC.toFixed(4);
sideAInput.value = “”; // Clear the side A input
} else {
resultDiv.innerHTML = “Error: Hypotenuse (C) must be greater than Side B.“;
return;
}
} else if (!isNaN(sideA) && !isNaN(sideB) && !isNaN(hypotenuseC) && sideA > 0 && sideB > 0 && hypotenuseC > 0) {
// Check if the provided values form a right triangle
var tolerance = 0.0001; // For floating point comparisons
if (Math.abs((sideA * sideA + sideB * sideB) – (hypotenuseC * hypotenuseC)) < tolerance) {
resultDiv.innerHTML = "The provided sides form a valid right-angled triangle.“;
} else {
resultDiv.innerHTML = “The provided sides do NOT form a valid right-angled triangle.“;
}
} else {
resultDiv.innerHTML = “Please enter at least two valid positive side lengths.“;
}
}