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);
width: 100%;
max-width: 700px;
margin-bottom: 30px;
}
h1, h2 {
color: #004a99;
text-align: center;
margin-bottom: 20px;
}
.input-group {
margin-bottom: 20px;
display: flex;
flex-direction: column;
align-items: flex-start;
}
.input-group label {
display: block;
margin-bottom: 8px;
font-weight: bold;
color: #555;
}
.input-group input[type=”number”] {
width: 100%;
padding: 12px;
border: 1px solid #ccc;
border-radius: 4px;
box-sizing: border-box;
font-size: 1rem;
}
.input-group input[type=”number”]:focus {
border-color: #004a99;
outline: none;
box-shadow: 0 0 0 3px rgba(0, 74, 153, 0.2);
}
button {
background-color: #004a99;
color: white;
padding: 12px 25px;
border: none;
border-radius: 4px;
cursor: pointer;
font-size: 1.1rem;
transition: background-color 0.3s ease;
width: 100%;
margin-top: 10px;
}
button:hover {
background-color: #003366;
}
#result {
margin-top: 25px;
padding: 20px;
background-color: #e7f3ff;
border-left: 5px solid #28a745;
border-radius: 4px;
font-size: 1.5rem;
font-weight: bold;
color: #004a99;
text-align: center;
}
#result span {
color: #28a745;
}
.article-container {
background-color: #ffffff;
padding: 30px;
border-radius: 8px;
box-shadow: 0 4px 15px rgba(0, 0, 0, 0.1);
width: 100%;
max-width: 700px;
}
.article-container h2 {
text-align: left;
color: #004a99;
margin-bottom: 15px;
}
.article-container p, .article-container ul {
margin-bottom: 15px;
}
.article-container strong {
color: #004a99;
}
@media (max-width: 600px) {
.loan-calc-container, .article-container {
padding: 20px;
}
h1 {
font-size: 1.8rem;
}
button {
font-size: 1rem;
}
#result {
font-size: 1.3rem;
}
}
Hypotenuse Length Calculator
Understanding the Hypotenuse and Its Calculation
The hypotenuse is a fundamental concept in geometry, specifically related to right-angled triangles. A right-angled triangle is a triangle where one of the interior angles measures exactly 90 degrees. The side opposite the right angle is always the longest side and is called the hypotenuse. The other two sides are known as the legs or cathetus.
The relationship between the lengths of the sides of a right-angled triangle is elegantly defined by the Pythagorean theorem, named after the ancient Greek mathematician Pythagoras. This theorem states that the square of the length of the hypotenuse (let’s call it ‘c’) is equal to the sum of the squares of the lengths of the other two sides (let’s call them ‘a’ and ‘b’).
Mathematically, this is expressed as:
a² + b² = c²
To find the length of the hypotenuse (‘c’) when the lengths of the two legs (‘a’ and ‘b’) are known, we need to rearrange the formula to solve for ‘c’:
c = √(a² + b²)
Our calculator uses this exact formula. You simply input the lengths of the two shorter sides (the legs) of the right-angled triangle, and it will compute the length of the hypotenuse for you.
Use Cases for Calculating the Hypotenuse:
- Construction and Carpentry: Determining the length of diagonal braces, roof rafters, or stair stringers.
- Navigation: Calculating the shortest distance between two points on a map when movement is restricted to north-south and east-west directions (forming a right triangle).
- Engineering: Calculating distances, forces, or components in various structural and mechanical designs.
- Surveying: Measuring distances across obstacles or calculating property boundaries.
- Computer Graphics and Game Development: Determining distances between objects or points in 2D or 3D space.
- Everyday Problem Solving: Figuring out if an object will fit through a diagonal opening or calculating the length of a slide in a playground.
By understanding and utilizing the Pythagorean theorem, you can solve a wide array of practical geometric problems. This calculator is a simple tool to quickly perform these calculations accurately.
function calculateHypotenuse() {
var sideAInput = document.getElementById(“sideA”);
var sideBInput = document.getElementById(“sideB”);
var resultDiv = document.getElementById(“result”);
var sideA = parseFloat(sideAInput.value);
var sideB = parseFloat(sideBInput.value);
if (isNaN(sideA) || isNaN(sideB) || sideA <= 0 || sideB <= 0) {
resultDiv.innerHTML = "Please enter valid positive numbers for both sides.";
resultDiv.style.color = "#dc3545"; // Red for error
resultDiv.style.borderColor = "#dc3545";
return;
}
var hypotenuseSquared = (sideA * sideA) + (sideB * sideB);
var hypotenuse = Math.sqrt(hypotenuseSquared);
resultDiv.innerHTML = "Hypotenuse Length: ” + hypotenuse.toFixed(4) + ” units“;
resultDiv.style.color = “#004a99”; // Primary blue for result
resultDiv.style.borderColor = “#28a745”; // Success green border
}