Sss Triangle Calculator

SSS Triangle Calculator







function calculateTriangleProperties() { var sideA = parseFloat(document.getElementById('sideA').value); var sideB = parseFloat(document.getElementById('sideB').value); var sideC = parseFloat(document.getElementById('sideC').value); var resultDiv = document.getElementById('result'); resultDiv.innerHTML = "; // Clear previous results if (isNaN(sideA) || isNaN(sideB) || isNaN(sideC) || sideA <= 0 || sideB <= 0 || sideC sideC) && (sideA + sideC > sideB) && (sideB + sideC > sideA))) { resultDiv.innerHTML = 'The given side lengths do not form a valid triangle (Triangle Inequality Theorem).'; return; } // Calculate Perimeter var perimeter = sideA + sideB + sideC; // Calculate Semi-perimeter var s = perimeter / 2; // Calculate Area using Heron's Formula var area = Math.sqrt(s * (s – sideA) * (s – sideB) * (s – sideC)); // Calculate Angles using Law of Cosines // Angle A (opposite sideA) 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 sideB) 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 sideC) 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); resultDiv.innerHTML += '

Triangle Properties:

'; resultDiv.innerHTML += 'Perimeter: ' + perimeter.toFixed(2) + ' units'; resultDiv.innerHTML += 'Area: ' + area.toFixed(2) + ' square units'; resultDiv.innerHTML += 'Angle A: ' + angleA_deg.toFixed(2) + ' degrees'; resultDiv.innerHTML += 'Angle B: ' + angleB_deg.toFixed(2) + ' degrees'; resultDiv.innerHTML += 'Angle C: ' + angleC_deg.toFixed(2) + ' degrees'; resultDiv.innerHTML += '(Sum of angles: ' + (angleA_deg + angleB_deg + angleC_deg).toFixed(2) + ' degrees)'; } .calculator-container { font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif; background-color: #f9f9f9; padding: 20px; border-radius: 8px; box-shadow: 0 2px 10px rgba(0, 0, 0, 0.1); max-width: 600px; margin: 20px auto; border: 1px solid #ddd; } .calculator-container h2 { text-align: center; color: #333; margin-bottom: 20px; } .calculator-inputs label { display: inline-block; margin-bottom: 8px; font-weight: bold; width: 120px; color: #555; } .calculator-inputs input[type="number"] { width: calc(100% – 140px); padding: 10px; margin-bottom: 10px; border: 1px solid #ccc; border-radius: 4px; box-sizing: border-box; } .calculator-inputs button { display: block; width: 100%; padding: 12px; background-color: #007bff; color: white; border: none; border-radius: 4px; font-size: 16px; cursor: pointer; transition: background-color 0.3s ease; margin-top: 15px; } .calculator-inputs button:hover { background-color: #0056b3; } .calculator-result { margin-top: 25px; padding: 15px; background-color: #e9f7ef; border: 1px solid #d4edda; border-radius: 5px; color: #155724; } .calculator-result h3 { color: #007bff; margin-top: 0; border-bottom: 1px solid #a2d9c0; padding-bottom: 10px; margin-bottom: 15px; } .calculator-result p { margin-bottom: 8px; line-height: 1.5; } .calculator-result p strong { color: #333; }

Understanding SSS Triangles and Their Properties

The SSS (Side-Side-Side) Triangle Calculator is a powerful tool for determining the various properties of a triangle when you know the lengths of all three of its sides. This method is fundamental in geometry and has wide-ranging applications in fields like engineering, architecture, surveying, and even computer graphics.

What is an SSS Triangle?

An SSS triangle refers to a triangle where the lengths of all three sides (Side A, Side B, and Side C) are known. With these three pieces of information, it's possible to uniquely define the triangle's shape and size, allowing us to calculate its angles, area, and perimeter.

How to Use the SSS Triangle Calculator

  1. Enter Side Lengths: Input the numerical values for the lengths of Side A, Side B, and Side C into the respective fields. Ensure these are positive numbers.
  2. Click "Calculate": Press the "Calculate Triangle Properties" button.
  3. View Results: The calculator will instantly display the triangle's perimeter, area, and the measures of its three interior angles (Angle A, Angle B, and Angle C) in degrees.

Important Note: Not every set of three lengths can form a triangle. The calculator will validate your inputs using the Triangle Inequality Theorem. This theorem 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 your inputs violate this rule, the calculator will inform you that a valid triangle cannot be formed.

Formulas Used in the Calculation

1. Perimeter

The perimeter (P) of a triangle is simply the sum of the lengths of its three sides:

P = Side A + Side B + Side C

2. Area (Heron's Formula)

When only the side lengths are known, Heron's Formula is used to calculate the area (A) of the triangle. First, we need to calculate the semi-perimeter (s), which is half of the perimeter:

s = P / 2

Then, the area is given by:

Area = √(s * (s - Side A) * (s - Side B) * (s - Side C))

3. Angles (Law of Cosines)

The Law of Cosines is essential for finding the interior angles of a triangle when all three side lengths are known. For a triangle with sides a, b, c and opposite angles A, B, C respectively:

  • To find Angle A:
    cos(A) = (Side B² + Side C² - Side A²) / (2 * Side B * Side C)
    Angle A = arccos(cos(A)) (converted to degrees)
  • To find Angle B:
    cos(B) = (Side A² + Side C² - Side B²) / (2 * Side A * Side C)
    Angle B = arccos(cos(B)) (converted to degrees)
  • To find Angle C:
    cos(C) = (Side A² + Side B² - Side C²) / (2 * Side A * Side B)
    Angle C = arccos(cos(C)) (converted to degrees)

The sum of the three angles in any Euclidean triangle should always be approximately 180 degrees. Small deviations in the sum might occur due to floating-point precision in calculations.

Example Calculation

Let's consider a triangle with the following side lengths:

  • Side A = 3 units
  • Side B = 4 units
  • Side C = 5 units

This is a classic example of a right-angled triangle (a Pythagorean triple).

  1. Perimeter:
    P = 3 + 4 + 5 = 12 units
  2. Semi-perimeter (s):
    s = 12 / 2 = 6 units
  3. Area:
    Area = √(6 * (6 - 3) * (6 - 4) * (6 - 5))
    Area = √(6 * 3 * 2 * 1)
    Area = √36 = 6 square units
  4. Angles:
    • Angle A:
      cos(A) = (4² + 5² - 3²) / (2 * 4 * 5) = (16 + 25 - 9) / 40 = 32 / 40 = 0.8
      Angle A ≈ 36.87°
    • Angle B:
      cos(B) = (3² + 5² - 4²) / (2 * 3 * 5) = (9 + 25 - 16) / 30 = 18 / 30 = 0.6
      Angle B ≈ 53.13°
    • Angle C:
      cos(C) = (3² + 4² - 5²) / (2 * 3 * 4) = (9 + 16 - 25) / 24 = 0 / 24 = 0
      Angle C = 90°

The SSS Triangle Calculator simplifies these complex calculations, providing quick and accurate results for any valid set of three side lengths.

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