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');
var angleAResult = document.getElementById('angleAResult');
var angleBResult = document.getElementById('angleBResult');
var angleCResult = document.getElementById('angleCResult');
var triangleTypeResult = document.getElementById('triangleTypeResult');
angleAResult.innerHTML = 'Angle A: -';
angleBResult.innerHTML = 'Angle B: -';
angleCResult.innerHTML = 'Angle C: -';
triangleTypeResult.innerHTML = 'Triangle Type: -';
if (isNaN(sideA) || isNaN(sideB) || isNaN(sideC) || sideA <= 0 || sideB <= 0 || sideC <= 0) {
resultDiv.style.color = 'red';
angleAResult.innerHTML = 'Error: Please enter valid positive numbers for all side lengths.';
angleBResult.innerHTML = ";
angleCResult.innerHTML = ";
triangleTypeResult.innerHTML = ";
return;
}
// Triangle Inequality Theorem check
if (!((sideA + sideB > sideC) && (sideA + sideC > sideB) && (sideB + sideC > sideA))) {
resultDiv.style.color = 'red';
angleAResult.innerHTML = 'Error: These side lengths cannot form a triangle (Triangle Inequality Theorem violated).';
angleBResult.innerHTML = ";
angleCResult.innerHTML = ";
triangleTypeResult.innerHTML = ";
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);
// Ensure values are within [-1, 1] for Math.acos to prevent NaN due to 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 angleA_rad = Math.acos(cosA);
var angleB_rad = Math.acos(cosB);
var angleC_rad = Math.acos(cosC);
var angleA_deg = angleA_rad * (180 / Math.PI);
var angleB_deg = angleB_rad * (180 / Math.PI);
var angleC_deg = angleC_rad * (180 / Math.PI);
// Round to 2 decimal places
angleA_deg = angleA_deg.toFixed(2);
angleB_deg = angleB_deg.toFixed(2);
angleC_deg = angleC_deg.toFixed(2);
// Determine triangle type based on angles
var type = ";
if (angleA_deg == 90 || angleB_deg == 90 || angleC_deg == 90) {
type = 'Right Triangle';
} else if (angleA_deg > 90 || angleB_deg > 90 || angleC_deg > 90) {
type = 'Obtuse Triangle';
} else {
type = 'Acute Triangle';
}
// Also check for equilateral/isosceles based on sides
if (sideA === sideB && sideB === sideC) {
type += ' (Equilateral)';
} else if (sideA === sideB || sideA === sideC || sideB === sideC) {
type += ' (Isosceles)';
} else {
type += ' (Scalene)';
}
resultDiv.style.color = '#333';
angleAResult.innerHTML = 'Angle A: ' + angleA_deg + '°';
angleBResult.innerHTML = 'Angle B: ' + angleB_deg + '°';
angleCResult.innerHTML = 'Angle C: ' + angleC_deg + '°';
triangleTypeResult.innerHTML = 'Triangle Type: ' + type;
}
Understanding Triangle Angles
A triangle is one of the most fundamental shapes 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 internal angles, which is crucial in various fields from architecture to surveying.
How the Calculator Works: The Law of Cosines
This calculator uses the Law of Cosines, a powerful formula that relates the lengths of the sides of a triangle to the cosine of one of its angles. If you know all three side lengths (let's call them a, b, and c), you can find each angle using the following formulas:
To find Angle A (opposite side a):cos(A) = (b² + c² - a²) / (2bc)
To find Angle B (opposite side b):cos(B) = (a² + c² - b²) / (2ac)
To find Angle C (opposite side c):cos(C) = (a² + b² - c²) / (2ab)
Once you have the cosine of an angle, you use the inverse cosine function (arccos or acos) to find the angle itself, typically converted from radians to degrees for easier understanding.
The Triangle Inequality Theorem
Before calculating angles, it's essential to ensure that the given side lengths can actually form a triangle. This is governed by the Triangle Inequality Theorem, which 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, the calculator will inform you that a triangle cannot be formed.
a + b > c
a + c > b
b + c > a
Types of Triangles by Angles
Based on their angles, triangles can be classified into three main types:
Acute Triangle: All three angles are less than 90 degrees.
Right Triangle: One angle is exactly 90 degrees.
Obtuse Triangle: One angle is greater than 90 degrees.
The calculator will also identify the type of triangle based on the calculated angles.
How to Use This Calculator
Enter Side Lengths: Input the lengths of the three sides of your triangle into the "Side A Length", "Side B Length", and "Side C Length" fields. Ensure these are positive numerical values.
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, along with the type of triangle (e.g., Right Scalene, Acute Isosceles).
Example Calculation
Let's say you have a triangle with the following side lengths:
Side A = 3 units
Side B = 4 units
Side C = 5 units
Inputting these values into the calculator will yield:
Angle A: Approximately 36.87°
Angle B: Approximately 53.13°
Angle C: Approximately 90.00°
Triangle Type: Right Scalene Triangle
This is a classic example of a 3-4-5 right triangle, where the angle opposite the longest side (Side C) is 90 degrees.