Angle Calculator Triangle

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Triangle Angle Calculator (SSS)

Results:

Angle A:

Angle B:

Angle C:

function calculateTriangleAngles() { var sideA = parseFloat(document.getElementById('sideALength').value); var sideB = parseFloat(document.getElementById('sideBLength').value); var sideC = parseFloat(document.getElementById('sideCLength').value); var angleAOutput = document.getElementById('angleAOutput'); var angleBOutput = document.getElementById('angleBOutput'); var angleCOutput = document.getElementById('angleCOutput'); var errorOutput = document.getElementById('errorOutput'); angleAOutput.innerHTML = 'Angle A: '; angleBOutput.innerHTML = 'Angle B: '; angleCOutput.innerHTML = 'Angle C: '; errorOutput.innerHTML = "; if (isNaN(sideA) || isNaN(sideB) || isNaN(sideC) || sideA <= 0 || sideB <= 0 || sideC sideC) && (sideA + sideC > sideB) && (sideB + sideC > sideA))) { errorOutput.innerHTML = 'The given side lengths do not form a valid triangle (Triangle Inequality Theorem violated).'; 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); // Due to floating point precision, cos values might be slightly outside [-1, 1] 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).toFixed(2); var angleB_deg = (angleB_rad * 180 / Math.PI).toFixed(2); var angleC_deg = (angleC_rad * 180 / Math.PI).toFixed(2); angleAOutput.innerHTML = 'Angle A: ' + angleA_deg + '°'; angleBOutput.innerHTML = 'Angle B: ' + angleB_deg + '°'; angleCOutput.innerHTML = 'Angle C: ' + angleC_deg + '°'; }

Understanding the Triangle Angle Calculator

A triangle angle calculator is a specialized tool designed to determine the interior angles of a triangle when certain information, such as the lengths of its sides, is known. This particular calculator focuses on the Side-Side-Side (SSS) case, where you provide the lengths of all three sides, and it computes the corresponding angles.

How it Works: The Law of Cosines

The core mathematical principle behind this calculator is the Law of Cosines. This fundamental theorem in trigonometry relates the lengths of the sides of a triangle to the cosine of one of its angles. For a triangle with sides a, b, and c, and angles A, B, and C opposite those respective sides, 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 to solve for the cosine of each angle:

  • cos(A) = (b² + c² - a²) / (2bc)
  • cos(B) = (a² + c² - b²) / (2ac)
  • cos(C) = (a² + b² - c²) / (2ab)

Once we have the cosine value, we use the inverse cosine function (arccos or cos⁻¹) to find the angle in radians, which is then converted to degrees for easier understanding.

The Triangle Inequality Theorem

Before calculating angles, the calculator first verifies if the given side lengths can actually form a triangle. This is done using 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 valid triangle cannot be formed.

  • a + b > c
  • a + c > b
  • b + c > a

How to Use the Calculator

  1. Enter Side A Length: Input the length of the first side of your triangle into the "Side A Length" field.
  2. Enter Side B Length: Input the length of the second side into the "Side B Length" field.
  3. Enter Side C Length: Input the length of the third side into the "Side C Length" field.
  4. Click "Calculate Angles": Press the button to see the computed angles.
  5. View Results: The calculator will display Angle A, Angle B, and Angle C in degrees. If the sides do not form a valid triangle, an error message will appear.

Example Calculation

Let's say you have a triangle with the following side lengths:

  • Side A = 5 units
  • Side B = 7 units
  • Side C = 9 units

Using the calculator with these values:

  • Angle A: Approximately 33.56°
  • Angle B: Approximately 51.32°
  • Angle C: Approximately 95.12°

(Note: The sum of the angles should always be 180° for a planar triangle, with minor deviations due to rounding.)

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