Angle Calculator Triangle

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Triangle Angle Calculator (SSS)

Calculated Angles:

Angle A: degrees

Angle B: degrees

Angle C: degrees

function calculateTriangleAngles() { var sideA = parseFloat(document.getElementById('sideA').value); var sideB = parseFloat(document.getElementById('sideB').value); var sideC = parseFloat(document.getElementById('sideC').value); var errorMessage = document.getElementById('errorMessage'); var angleA_display = document.getElementById('angleA'); var angleB_display = document.getElementById('angleB'); var angleC_display = document.getElementById('angleC'); var triangleSum_display = document.getElementById('triangleSum'); errorMessage.textContent = "; angleA_display.textContent = "; angleB_display.textContent = "; angleC_display.textContent = "; triangleSum_display.textContent = "; if (isNaN(sideA) || isNaN(sideB) || isNaN(sideC) || sideA <= 0 || sideB <= 0 || sideC sideC) && (sideA + sideC > sideB) && (sideB + sideC > sideA))) { errorMessage.textContent = 'These side lengths do not form a valid triangle (Triangle Inequality Theorem not met).'; return; } // Law of Cosines to find angles // Angle A (opposite side a) var cosA = (sideB * sideB + sideC * sideC – sideA * sideA) / (2 * sideB * sideC); var angleA_rad = Math.acos(cosA); var angleA_deg = angleA_rad * (180 / Math.PI); // Angle B (opposite side b) var cosB = (sideA * sideA + sideC * sideC – sideB * sideB) / (2 * sideA * sideC); var angleB_rad = Math.acos(cosB); var angleB_deg = angleB_rad * (180 / Math.PI); // Angle C (opposite side c) var cosC = (sideA * sideA + sideB * sideB – sideC * sideC) / (2 * sideA * sideB); var angleC_rad = Math.acos(cosC); var angleC_deg = angleC_rad * (180 / Math.PI); // Display results angleA_display.textContent = angleA_deg.toFixed(2); angleB_display.textContent = angleB_deg.toFixed(2); angleC_display.textContent = angleC_deg.toFixed(2); var sumOfAngles = angleA_deg + angleB_deg + angleC_deg; triangleSum_display.textContent = 'Sum of angles: ' + sumOfAngles.toFixed(2) + ' degrees (should be 180)'; } // Initial calculation on page load for default values window.onload = calculateTriangleAngles;

Understanding the Triangle Angle Calculator

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. This Triangle Angle Calculator helps you determine the measure of each interior angle of a triangle when you know the lengths of all three sides.

How it Works: The Law of Cosines

This calculator utilizes the Law of Cosines, a powerful formula in trigonometry that 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:

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

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

The Triangle Inequality Theorem

Not just any three lengths can form a triangle. For a valid triangle to exist, the sum of the lengths of any two sides must be greater than the length of the third side. This is known as the Triangle Inequality Theorem. The calculator checks this condition:

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

If these conditions are not met, the calculator will inform you that the given side lengths cannot form a triangle.

How to Use the Calculator

  1. Enter Side A Length: Input the length of the first side of your triangle.
  2. Enter Side B Length: Input the length of the second side.
  3. Enter Side C Length: Input the length of the third side.
  4. Click "Calculate Angles": The calculator will instantly display the measures of Angle A, Angle B, and Angle C in degrees. Angle A is opposite Side A, Angle B opposite Side B, and Angle C opposite Side C.

Realistic Examples

Let's look at some common triangle types:

Example 1: Right-Angled Triangle (3-4-5)

Consider a classic right-angled triangle with sides 3, 4, and 5 units. Let a=3, b=4, c=5.

  • Side A: 3
  • Side B: 4
  • Side C: 5

The calculator would output approximately:

  • Angle A: 36.87 degrees
  • Angle B: 53.13 degrees
  • Angle C: 90.00 degrees

Notice that Angle C is 90 degrees, confirming it's a right triangle.

Example 2: Equilateral Triangle

An equilateral triangle has all three sides equal. Let a=10, b=10, c=10.

  • Side A: 10
  • Side B: 10
  • Side C: 10

The calculator would output:

  • Angle A: 60.00 degrees
  • Angle B: 60.00 degrees
  • Angle C: 60.00 degrees

As expected, all angles are 60 degrees, summing to 180 degrees.

Example 3: Isosceles Triangle

An isosceles triangle has two sides of equal length. Let a=7, b=7, c=5.

  • Side A: 7
  • Side B: 7
  • Side C: 5

The calculator would output approximately:

  • Angle A: 69.51 degrees
  • Angle B: 69.51 degrees
  • Angle C: 40.98 degrees

Angles A and B are equal, as they are opposite the equal sides.

This tool is invaluable for students, engineers, architects, and anyone working with geometric problems involving triangles.

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