Right-Angled Triangle (Pythagorean)
General Triangle (Side-Angle-Side)
Calculation Result
0
How to Calculate Triangle Sides
Whether you are working on a geometry assignment or a DIY home improvement project, finding the third side of a triangle is a common mathematical task. Our Triangle Side Calculator uses two primary mathematical principles depending on the information you have: the Pythagorean Theorem and the Law of Cosines.
1. Right-Angled Triangles (Pythagorean Theorem)
If you have a right triangle (where one angle is exactly 90 degrees), you can use the Pythagorean Theorem to find the hypotenuse (the side opposite the right angle). The formula is:
a² + b² = c²
Where a and b are the legs of the triangle and c is the longest side.
2. General Triangles (Law of Cosines)
If the triangle is not a right triangle, but you know two sides and the angle between them (SAS – Side-Angle-Side), you use the Law of Cosines:
c² = a² + b² – 2ab · cos(γ)
Where γ (gamma) is the angle between sides a and b.
Practical Examples
Construction: If you are building a rectangular deck and want to ensure it is square, you can measure side A (3 meters) and side B (4 meters). The diagonal (side C) should be exactly 5 meters if the corners are 90 degrees.
Roofing: To find the length of a rafter, you measure the horizontal run and the vertical rise. The rafter represents the hypotenuse of a right triangle.
Landscaping: If you have a triangular garden bed where two sides meet at a 60-degree angle, you can use the SAS method to determine the length of the third side for fencing.
function toggleInputs() {
var mode = document.getElementById("calcMode").value;
var angleDiv = document.getElementById("inputGroupAngle");
if (mode === "sas") {
angleDiv.style.display = "block";
} else {
angleDiv.style.display = "none";
}
}
function calculateTriangle() {
var mode = document.getElementById("calcMode").value;
var a = parseFloat(document.getElementById("sideA").value);
var b = parseFloat(document.getElementById("sideB").value);
var resultDiv = document.getElementById("resultDisplay");
var resultText = document.getElementById("finalResult");
var methodText = document.getElementById("methodUsed");
if (isNaN(a) || isNaN(b) || a <= 0 || b <= 0) {
alert("Please enter valid positive numbers for side lengths.");
return;
}
var c = 0;
if (mode === "right") {
// Pythagorean Theorem: c = sqrt(a^2 + b^2)
c = Math.sqrt(Math.pow(a, 2) + Math.pow(b, 2));
methodText.innerText = "Calculated using Pythagorean Theorem (a² + b² = c²)";
} else {
// Law of Cosines: c = sqrt(a^2 + b^2 – 2ab*cos(angle))
var angleDeg = parseFloat(document.getElementById("angleC").value);
if (isNaN(angleDeg) || angleDeg = 180) {
alert("Please enter a valid angle between 0 and 180 degrees.");
return;
}
var angleRad = angleDeg * (Math.PI / 180);
c = Math.sqrt(Math.pow(a, 2) + Math.pow(b, 2) – (2 * a * b * Math.cos(angleRad)));
methodText.innerText = "Calculated using Law of Cosines (Side-Angle-Side)";
}
if (isNaN(c)) {
resultText.innerText = "Invalid Triangle";
methodText.innerText = "The dimensions provided do not form a valid triangle.";
} else {
resultText.innerText = "Side C = " + c.toFixed(4);
}
resultDiv.style.display = "block";
}