Calculate the length of the hypotenuse of a right-angled triangle using the lengths of the other two sides (legs).
Hypotenuse (c) will appear here.
Understanding the Hypotenuse
The hypotenuse is a fundamental concept in geometry, particularly when dealing with right-angled triangles. A right-angled triangle is a triangle that has one angle measuring exactly 90 degrees. The sides adjacent to the right angle are called "legs" (often denoted as 'a' and 'b'), and the side opposite the right angle is called the "hypotenuse" (denoted as 'c'). The hypotenuse is always the longest side of a right-angled triangle.
The relationship between the lengths of the legs and the hypotenuse of a right-angled triangle is described by the famous Pythagorean Theorem.
The Pythagorean Theorem
The Pythagorean Theorem states that in any right-angled triangle, 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, this is expressed as:
a² + b² = c²
To find the length of the hypotenuse (c), we can rearrange the formula to solve for c:
c = √(a² + b²)
How the Calculator Works
This calculator uses the Pythagorean Theorem to find the hypotenuse. You simply need to input the lengths of the two legs (Side A and Side B) of the right-angled triangle into the fields above. The calculator will then perform the following steps:
Square the value of Side A (a²).
Square the value of Side B (b²).
Add the two squared values together (a² + b²).
Calculate the square root of the sum to find the length of the hypotenuse (c).
Use Cases for the Hypotenuse Calculator
The ability to calculate the hypotenuse is useful in various fields:
Construction and Carpentry: Determining the length of diagonal braces, roof rafters, or stair stringers.
Navigation: Calculating the shortest distance between two points when traveling along perpendicular paths.
Engineering: Designing structures and calculating forces.
Computer Graphics: Used in algorithms for calculating distances and positions.
Everyday Problem Solving: Figuring out if a large object will fit through a doorway diagonally, or determining the length of a ramp.
By entering the lengths of the two shorter sides, you can quickly and accurately find the length of the longest side, the hypotenuse, with this reliable tool.
function calculateHypotenuse() {
var sideA = parseFloat(document.getElementById("sideA").value);
var sideB = parseFloat(document.getElementById("sideB").value);
var resultDiv = document.getElementById("result");
if (isNaN(sideA) || isNaN(sideB)) {
resultDiv.innerHTML = "Please enter valid numbers for both sides.";
return;
}
if (sideA <= 0 || sideB <= 0) {
resultDiv.innerHTML = "Side lengths must be positive numbers.";
return;
}
var hypotenuseSquared = (sideA * sideA) + (sideB * sideB);
var hypotenuse = Math.sqrt(hypotenuseSquared);
resultDiv.innerHTML = "Hypotenuse (c): " + hypotenuse.toFixed(4) + "";
}