Calculate Triangle Angles

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Triangle Angle Calculator

Enter two angles of a triangle to find the third angle.

Result:

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Understanding Triangle Angles

Triangles are fundamental geometric shapes with 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 forms the basis for calculating any unknown angle when two angles are known.

This calculator helps you quickly determine the measure of the third angle of a triangle, given the measures of the other two angles.

The Math Behind It

Let the three interior angles of a triangle be denoted by $A$, $B$, and $C$. The fundamental property states:

$A + B + C = 180^\circ$

If you know two angles, say $A$ and $B$, you can find the third angle, $C$, by rearranging the formula:

$C = 180^\circ – (A + B)$

How to Use the Calculator

  1. Enter the measure of the first known angle in degrees into the "Angle 1 (degrees)" field.
  2. Enter the measure of the second known angle in degrees into the "Angle 2 (degrees)" field.
  3. Click the "Calculate Third Angle" button.
  4. The calculated measure of the third angle will be displayed.

Important Considerations

  • Valid Triangle: For a valid triangle to exist, each angle must be greater than 0 degrees, and the sum of any two angles must be less than 180 degrees. This calculator checks for basic validity (angles > 0 and sum < 180).
  • Units: The calculator assumes angles are provided in degrees.
  • Types of Triangles:
    • Acute Triangle: All angles are less than 90 degrees.
    • Obtuse Triangle: One angle is greater than 90 degrees.
    • Right Triangle: One angle is exactly 90 degrees.
    • Equilateral Triangle: All three angles are 60 degrees.
    • Isosceles Triangle: Two angles are equal.
    • Scalene Triangle: All three angles are different.

Use Cases

  • Geometry Education: A practical tool for students learning about triangle properties.
  • Construction & Design: Useful for architects, engineers, and designers who work with angled structures.
  • Navigation & Surveying: Angles are crucial in determining positions and distances.
  • General Problem Solving: Any scenario involving triangles where angle relationships are important.

By understanding the simple rule that triangle angles sum to 180 degrees, you can solve for missing angles efficiently using this calculator.

function calculateThirdAngle() { var angle1Input = document.getElementById("angle1"); var angle2Input = document.getElementById("angle2"); var errorDisplay = document.getElementById("errorDisplay"); var resultDisplay = document.getElementById("angleResult"); // Clear previous results and errors resultDisplay.innerHTML = "–"; errorDisplay.innerHTML = ""; // Get input values and convert to numbers var angle1 = parseFloat(angle1Input.value); var angle2 = parseFloat(angle2Input.value); // Validate inputs if (isNaN(angle1) || isNaN(angle2)) { errorDisplay.innerHTML = "Please enter valid numbers for both angles."; return; } if (angle1 <= 0 || angle2 = 180) { errorDisplay.innerHTML = "The sum of the two given angles must be less than 180 degrees for a valid triangle."; return; } // Calculate the third angle var angle3 = 180 – sumOfTwoAngles; // Display the result resultDisplay.innerHTML = angle3.toFixed(2) + "°"; // Display with 2 decimal places and degree symbol }

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