A right triangle is a fundamental geometric shape consisting of three sides and three angles, where one of the angles is exactly 90 degrees (a right angle). The sides of a right triangle have specific names based on their position relative to the right angle:
Legs (or Cathetus): These are the two sides that form the right angle. In our calculator, these are referred to as Side A and Side B.
Hypotenuse: This is the side opposite the right angle. It is always the longest side of a right triangle. In our calculator, this is referred to as Side C.
The Pythagorean Theorem
The relationship between the sides of a right triangle is elegantly described by the Pythagorean Theorem. This 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 (the legs).
Mathematically, this is expressed as:
a² + b² = c²
Where:
'a' and 'b' are the lengths of the two legs.
'c' is the length of the hypotenuse.
How This Calculator Works
This calculator utilizes the Pythagorean Theorem to find a missing side of a right triangle when two other sides are known. You need to provide the lengths of the sides you know, ensuring you correctly identify which is a leg and which is the hypotenuse if applicable. Then, select which side you want the calculator to determine.
To calculate the Hypotenuse (C): You must provide the lengths of Side A and Side B. The formula used is: c = √(a² + b²)
To calculate Side A: You must provide the length of Side B and the Hypotenuse (C). The formula used is: a = √(c² - b²)
To calculate Side B: You must provide the length of Side A and the Hypotenuse (C). The formula used is: b = √(c² - a²)
Use Cases
The ability to calculate sides of a right triangle is crucial in many fields:
Construction and Architecture: Ensuring corners are perfectly square, calculating diagonal braces, and determining roof slopes.
Navigation: Calculating distances and positions using coordinates.
Engineering: Designing structures, understanding forces, and solving problems in physics.
Surveying: Measuring distances and heights indirectly.
Graphic Design and Game Development: Positioning elements on a 2D plane.
Everyday Life: Figuring out if furniture will fit through a doorway diagonally or calculating the shortest path across a rectangular park.
By understanding and applying the Pythagorean Theorem, you can solve a wide range of practical and theoretical problems involving right-angled shapes.
function calculateSide() {
var sideAInput = document.getElementById("knownSideA");
var sideBInput = document.getElementById("knownSideB");
var sideCInput = document.getElementById("knownSideC");
var calculateWhat = document.getElementById("calculateWhat").value;
var resultDiv = document.getElementById("result");
var a = parseFloat(sideAInput.value);
var b = parseFloat(sideBInput.value);
var c = parseFloat(sideCInput.value);
var calculatedValue = NaN;
var errorMessage = "";
var resultText = "";
if (calculateWhat === "hypotenuse") {
if (!isNaN(a) && !isNaN(b) && a > 0 && b > 0) {
calculatedValue = Math.sqrt(a*a + b*b);
resultText = "Calculated Hypotenuse (C): " + calculatedValue.toFixed(4);
} else {
errorMessage = "Please enter positive values for Side A and Side B to calculate the hypotenuse.";
}
} else if (calculateWhat === "sideA") {
if (!isNaN(b) && !isNaN(c) && b > 0 && c > 0) {
if (c > b) {
calculatedValue = Math.sqrt(c*c – b*b);
resultText = "Calculated Side A: " + calculatedValue.toFixed(4);
} else {
errorMessage = "Hypotenuse (C) must be greater than Side B.";
}
} else {
errorMessage = "Please enter positive values for Side B and Hypotenuse (C) to calculate Side A.";
}
} else if (calculateWhat === "sideB") {
if (!isNaN(a) && !isNaN(c) && a > 0 && c > 0) {
if (c > a) {
calculatedValue = Math.sqrt(c*c – a*a);
resultText = "Calculated Side B: " + calculatedValue.toFixed(4);
} else {
errorMessage = "Hypotenuse (C) must be greater than Side A.";
}
} else {
errorMessage = "Please enter positive values for Side A and Hypotenuse (C) to calculate Side B.";
}
}
if (errorMessage) {
resultDiv.style.color = "#dc3545"; // Red for error
resultDiv.style.borderColor = "#dc3545";
resultDiv.innerHTML = errorMessage;
} else if (!isNaN(calculatedValue)) {
resultDiv.style.color = "#004a99"; // Primary blue for success
resultDiv.style.borderColor = "#28a745"; // Success green border
resultDiv.innerHTML = resultText;
} else {
resultDiv.style.color = "#dc3545";
resultDiv.style.borderColor = "#dc3545";
resultDiv.innerHTML = "Please provide valid inputs.";
}
}
function resetFields() {
document.getElementById("knownSideA").value = "";
document.getElementById("knownSideB").value = "";
document.getElementById("knownSideC").value = "";
document.getElementById("calculateWhat").value = "hypotenuse";
document.getElementById("result").innerHTML = "";
document.getElementById("result").style.color = "#004a99";
document.getElementById("result").style.borderColor = "#28a745";
}