function calculateTriangleAngles() {
var sideA = parseFloat(document.getElementById('sideA').value);
var sideB = parseFloat(document.getElementById('sideB').value);
var sideC = parseFloat(document.getElementById('sideC').value);
var resultDiv = document.getElementById('result');
resultDiv.style.display = 'none';
resultDiv.classList.remove('error');
if (isNaN(sideA) || isNaN(sideB) || isNaN(sideC) || sideA <= 0 || sideB <= 0 || sideC sideC) && (sideA + sideC > sideB) && (sideB + sideC > sideA))) {
resultDiv.innerHTML = 'These side lengths do not form a valid triangle. The sum of any two sides must be greater than the third side.';
resultDiv.classList.add('error');
resultDiv.style.display = 'block';
return;
}
// Law of Cosines to find angles
// cos(A) = (b^2 + c^2 – a^2) / (2bc)
// cos(B) = (a^2 + c^2 – b^2) / (2ac)
// cos(C) = (a^2 + b^2 – c^2) / (2ab)
var cosA = (sideB * sideB + sideC * sideC – sideA * sideA) / (2 * sideB * sideC);
var cosB = (sideA * sideA + sideC * sideC – sideB * sideB) / (2 * sideA * sideC);
var cosC = (sideA * sideA + sideB * sideB – sideC * sideC) / (2 * sideA * sideB);
// Clamp values to [-1, 1] due to potential floating point inaccuracies
cosA = Math.max(-1, Math.min(1, cosA));
cosB = Math.max(-1, Math.min(1, cosB));
cosC = Math.max(-1, Math.min(1, cosC));
var angleARad = Math.acos(cosA);
var angleBRad = Math.acos(cosB);
var angleCRad = Math.acos(cosC);
var angleADeg = angleARad * (180 / Math.PI);
var angleBDeg = angleBRad * (180 / Math.PI);
var angleCDeg = angleCRad * (180 / Math.PI);
var sumOfAngles = angleADeg + angleBDeg + angleCDeg;
resultDiv.innerHTML =
'Calculated Angles:' +
'Angle A (opposite Side A): ' + angleADeg.toFixed(2) + '°' +
'Angle B (opposite Side B): ' + angleBDeg.toFixed(2) + '°' +
'Angle C (opposite Side C): ' + angleCDeg.toFixed(2) + '°' +
'(Sum of angles: ' + sumOfAngles.toFixed(2) + '°)';
resultDiv.style.display = 'block';
}
Understanding Triangle Angles and the Law of Cosines
A triangle is a fundamental polygon in geometry, defined by three straight sides and three angles. The sum of the interior angles of any triangle always equals 180 degrees. Knowing the lengths of a triangle's sides allows us to determine the measure of each of its interior angles using a powerful trigonometric principle: the Law of Cosines.
What is the Law of Cosines?
The Law of Cosines is a generalization of the Pythagorean theorem that relates the lengths of the sides of a triangle to the cosine of one of its angles. It's particularly useful when you know all three side lengths (SSS – Side-Side-Side) and want to find the angles, or when you know two sides and the included angle (SAS – Side-Angle-Side) and want to find the third side.
For a triangle with sides a, b, and c, and angles A, B, and C opposite those sides respectively, the Law of Cosines states:
a² = b² + c² - 2bc ⋅ cos(A)
b² = a² + c² - 2ac ⋅ cos(B)
c² = a² + b² - 2ab ⋅ cos(C)
To find the angles, we rearrange these formulas:
cos(A) = (b² + c² - a²) / (2bc)
cos(B) = (a² + c² - b²) / (2ac)
cos(C) = (a² + b² - c²) / (2ab)
Once you have the cosine of an angle, you use the inverse cosine function (arccos or cos⁻¹) to find the angle itself, typically converted from radians to degrees.
The Triangle Inequality Theorem
Before calculating angles, it's crucial to ensure that the given side lengths can actually form a triangle. The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. If this condition is not met, a triangle cannot be formed with those side lengths.
a + b > c
a + c > b
b + c > a
How to Use This Calculator
Enter Side Lengths: Input the numerical values for the lengths of Side A, Side B, and Side C into the respective fields. These can be any positive real numbers.
Click "Calculate Angles": Press the button to initiate the calculation.
View Results: The calculator will display the measure of Angle A, Angle B, and Angle C in degrees. It will also show the sum of the angles, which should be approximately 180°.
Error Handling: If the inputs are invalid (e.g., non-numeric, zero, or negative) or if the side lengths do not form a valid triangle according to the Triangle Inequality Theorem, an error message will be displayed.
Example Calculation
Let's say you have a triangle with the following side lengths:
The sum of the angles is approximately 33.56° + 50.70° + 95.74° = 180.00°. This calculator automates these calculations for you, providing quick and accurate results.