Enter two angles of a triangle, and this calculator will find the third angle.
Understanding Triangle Angles
Triangles are fundamental geometric shapes consisting of three sides and three interior angles. A key property of all triangles in Euclidean geometry is that the sum of their interior angles always equals 180 degrees. This principle is known as the Triangle Angle Sum Theorem.
This calculator leverages this theorem to help you find a missing angle when two angles are known. Whether you're a student learning geometry, a surveyor, an architect, or a hobbyist working with designs, understanding and calculating triangle angles is a common and useful task.
How the Calculator Works
The calculator takes two known angles of a triangle (let's call them Angle A and Angle B) and calculates the third angle (Angle C) using the following formula derived from the Triangle Angle Sum Theorem:
Angle A + Angle B + Angle C = 180°
Therefore, to find Angle C, we rearrange the formula:
Angle C = 180° - (Angle A + Angle B)
The calculator first sums the two input angles. It then subtracts this sum from 180 to determine the value of the third angle. It also includes checks to ensure that the input angles are valid (positive numbers) and that their sum does not exceed 180 degrees, as this would not form a valid triangle.
Use Cases for Triangle Angle Calculations
Geometry Education: Essential for solving problems in textbooks and understanding geometric principles.
Navigation and Surveying: Calculating bearings and distances often involves triangulation.
Architecture and Engineering: Designing structures, calculating roof pitches, and ensuring stability.
Computer Graphics: Used in rendering 3D models and creating visual effects.
Art and Design: Planning layouts, creating patterns, and understanding perspective.
Physics: Analyzing forces, vectors, and wave phenomena.
Important Considerations
Units: This calculator assumes angles are measured in degrees.
Valid Triangles: For a valid triangle, all angles must be positive, and their sum must be exactly 180 degrees. If the sum of the two provided angles is 180 degrees or more, or if either angle is zero or negative, it's impossible to form a triangle.
Types of Triangles: The calculated angles can help identify the type of triangle:
Acute Triangle: All angles are less than 90°.
Right Triangle: One angle is exactly 90°.
Obtuse Triangle: One angle is greater than 90°.
Equilateral Triangle: All angles are 60°.
Isosceles Triangle: At least two angles are equal.
function calculateThirdAngle() {
var angleAInput = document.getElementById("angleA");
var angleBInput = document.getElementById("angleB");
var resultDiv = document.getElementById("result");
var errorDiv = document.getElementById("errorMessage");
// Clear previous results and errors
resultDiv.innerHTML = "";
errorDiv.innerHTML = "";
var angleA = parseFloat(angleAInput.value);
var angleB = parseFloat(angleBInput.value);
// Input validation
if (isNaN(angleA) || isNaN(angleB)) {
errorDiv.innerHTML = "Please enter valid numbers for both angles.";
return;
}
if (angleA <= 0 || angleB = 180) {
errorDiv.innerHTML = "The sum of the two angles must be less than 180 degrees to form a valid triangle.";
return;
}
var angleC = 180 – sumOfTwoAngles;
// Display the result
resultDiv.innerHTML = "Angle A: " + angleA.toFixed(2) + "°" +
"Angle B: " + angleB.toFixed(2) + "°" +
"Calculated Angle C: " + angleC.toFixed(2) + "°";
}