Enter two angles of a triangle, and this calculator will determine the third angle.
Third Angle:
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Understanding Triangle Angles
Triangles are fundamental geometric shapes consisting of three sides and three interior angles. A key property of all triangles, regardless of their shape or size, is that the sum of their three interior angles always equals 180 degrees. This principle is a cornerstone of Euclidean geometry and is derived from the parallel postulate.
This property allows us to easily calculate any missing angle if we know the values of the other two. Let the three interior angles of a triangle be denoted as Angle A, Angle B, and Angle C. The fundamental relationship is:
Angle A + Angle B + Angle C = 180°
Using this formula, if you know two angles, you can find the third by rearranging the equation:
Angle C = 180° - Angle A - Angle B
How the Calculator Works
Our Triangle Angles Calculator simplifies this process. You input the values (in degrees) for any two angles of a triangle into the provided fields. Upon clicking the 'Calculate Third Angle' button, the calculator performs the subtraction 180 - (Angle 1) - (Angle 2) to determine the measure of the third angle.
Use Cases
Geometry Education: Aiding students in understanding and applying the angle sum property of triangles.
Construction and Design: Architects and builders might use angle calculations for specific structural elements that form triangular shapes.
Navigation: In fields like surveying and navigation, calculating angles is crucial for determining positions and bearings.
Art and Craft: Artists and craftspeople creating geometric patterns or designs often need precise angle measurements.
Problem Solving: Quickly solving geometry problems that involve finding unknown angles in triangles.
Important Considerations:
The sum of any two entered angles must be less than 180 degrees for a valid triangle to exist.
Angles are typically measured in degrees for basic geometry. Ensure your input is in degrees.
The calculator assumes a Euclidean (flat) plane.
function calculateThirdAngle() {
var angle1Input = document.getElementById("angle1");
var angle2Input = document.getElementById("angle2");
var resultValueElement = document.getElementById("result-value");
var angle1 = parseFloat(angle1Input.value);
var angle2 = parseFloat(angle2Input.value);
var errorContainer = document.getElementById("result");
var errorMessage = "";
// Input Validation
if (isNaN(angle1) || isNaN(angle2)) {
errorMessage = "Please enter valid numbers for both angles.";
} else if (angle1 <= 0 || angle2 = 180 || angle2 >= 180) {
errorMessage = "Angles cannot be 180 degrees or more.";
} else if (angle1 + angle2 >= 180) {
errorMessage = "The sum of the two angles must be less than 180 degrees to form a valid triangle.";
}
if (errorMessage) {
resultValueElement.textContent = "Error";
resultValueElement.style.color = "red";
// Display error message in a more prominent way if needed, or just rely on the text
console.error(errorMessage); // Log error for debugging
} else {
var angle3 = 180 – angle1 – angle2;
resultValueElement.textContent = angle3.toFixed(2) + "°"; // Display with 2 decimal places and degree symbol
resultValueElement.style.color = "#0056b3"; // Reset to default success color
}
}