Sides of Triangle Calculator

Triangle Sides Calculator

Results:

function calculateTriangleProperties() { var sideA = parseFloat(document.getElementById('sideA').value); var sideB = parseFloat(document.getElementById('sideB').value); var sideC = parseFloat(document.getElementById('sideC').value); var canFormTriangleElem = document.getElementById('canFormTriangle'); var triangleTypeSidesElem = document.getElementById('triangleTypeSides'); var triangleTypeAnglesElem = document.getElementById('triangleTypeAngles'); var perimeterResultElem = document.getElementById('perimeterResult'); var areaResultElem = document.getElementById('areaResult'); // Reset results canFormTriangleElem.innerHTML = "; triangleTypeSidesElem.innerHTML = "; triangleTypeAnglesElem.innerHTML = "; perimeterResultElem.innerHTML = "; areaResultElem.innerHTML = "; if (isNaN(sideA) || isNaN(sideB) || isNaN(sideC) || sideA <= 0 || sideB <= 0 || sideC <= 0) { canFormTriangleElem.innerHTML = 'Please enter valid positive numbers for all side lengths.'; return; } // Triangle Inequality Theorem if (!((sideA + sideB > sideC) && (sideA + sideC > sideB) && (sideB + sideC > sideA))) { canFormTriangleElem.innerHTML = 'Cannot form a triangle with these side lengths (Triangle Inequality Theorem violated).'; return; } canFormTriangleElem.innerHTML = 'Can Form a Triangle: Yes'; // Determine type by sides var typeBySides = "; if (sideA === sideB && sideB === sideC) { typeBySides = 'Equilateral'; } else if (sideA === sideB || sideA === sideC || sideB === sideC) { typeBySides = 'Isosceles'; } else { typeBySides = 'Scalene'; } triangleTypeSidesElem.innerHTML = 'Type by Sides: ' + typeBySides; // Determine type by angles var sides = [sideA, sideB, sideC].sort(function(a, b) { return a – b; }); var aSq = sides[0] * sides[0]; var bSq = sides[1] * sides[1]; var cSq = sides[2] * sides[2]; var typeByAngles = "; var epsilon = 0.0001; // For floating point comparison if (Math.abs(aSq + bSq – cSq) cSq) { typeByAngles = 'Acute-angled'; } else { // aSq + bSq < cSq typeByAngles = 'Obtuse-angled'; } triangleTypeAnglesElem.innerHTML = 'Type by Angles: ' + typeByAngles; // Calculate Perimeter var perimeter = sideA + sideB + sideC; perimeterResultElem.innerHTML = 'Perimeter: ' + perimeter.toFixed(2); // Calculate Area (Heron's Formula) var s = perimeter / 2; // Semi-perimeter var areaSquared = s * (s – sideA) * (s – sideB) * (s – sideC); // Due to floating point inaccuracies, areaSquared might be slightly negative for valid triangles. // If it's very close to zero, treat it as zero. var area = 0; if (areaSquared >= -epsilon) { // Allow for very small negative values due to precision area = Math.sqrt(Math.max(0, areaSquared)); // Ensure we don't take sqrt of negative } areaResultElem.innerHTML = 'Area: ' + area.toFixed(2); }

Understanding Triangles with the Triangle Sides Calculator

A triangle is one of the most fundamental shapes in geometry, a polygon with three edges and three vertices. Despite its simple definition, triangles possess a rich set of properties that are crucial in various fields, from architecture and engineering to computer graphics and physics. Our Triangle Sides Calculator helps you explore these properties by simply inputting the lengths of its three sides.

The Triangle Inequality Theorem

Before any other calculations, the calculator first checks if the given side lengths can even form a valid triangle. This is governed by the Triangle Inequality Theorem, which states:

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 (a + b > c, a + c > b, and b + c > a) is not met, the calculator will inform you that a triangle cannot be formed.

Classifying Triangles by Side Lengths

Triangles can be categorized based on the lengths of their sides:

  • Equilateral Triangle: All three sides are equal in length (e.g., 5, 5, 5). All angles are also equal (60 degrees).
  • Isosceles Triangle: At least two sides are equal in length (e.g., 5, 5, 7). The angles opposite the equal sides are also equal.
  • Scalene Triangle: All three sides have different lengths (e.g., 3, 4, 5). All angles are also different.

Classifying Triangles by Angles

Beyond side lengths, triangles are also classified by their internal angles. The sum of the angles in any triangle is always 180 degrees. To determine the angle type from side lengths, we use a variation of the Pythagorean theorem. Let 'c' be the longest side and 'a' and 'b' be the other two sides:

  • Right-angled Triangle: If a² + b² = c². One angle is exactly 90 degrees. The classic example is a 3-4-5 triangle.
  • Acute-angled Triangle: If a² + b² > c². All three angles are less than 90 degrees.
  • Obtuse-angled Triangle: If a² + b² < c². One angle is greater than 90 degrees.

Perimeter and Area Calculations

The calculator also provides two fundamental measurements:

  • Perimeter: This is the total length of the boundary of the triangle. It's simply the sum of all three side lengths: P = a + b + c.
  • Area: This is the amount of space enclosed by the triangle. For calculating the area when only side lengths are known, Heron's Formula is used:
    First, calculate the semi-perimeter (s): s = (a + b + c) / 2
    Then, the Area (A) is: A = √[s(s - a)(s - b)(s - c)]

How to Use the Calculator

  1. Enter the length of Side A in the first input field.
  2. Enter the length of Side B in the second input field.
  3. Enter the length of Side C in the third input field.
  4. Click the "Calculate Triangle Properties" button.

The calculator will instantly display whether a triangle can be formed, its classification by sides and angles, its perimeter, and its area.

Examples:

Example 1: Right-angled Scalene Triangle

  • Side A: 3
  • Side B: 4
  • Side C: 5
  • Result: Can Form a Triangle: Yes, Type by Sides: Scalene, Type by Angles: Right-angled, Perimeter: 12.00, Area: 6.00

Example 2: Equilateral Triangle

  • Side A: 6
  • Side B: 6
  • Side C: 6
  • Result: Can Form a Triangle: Yes, Type by Sides: Equilateral, Type by Angles: Acute-angled, Perimeter: 18.00, Area: 15.59

Example 3: Invalid Triangle

  • Side A: 1
  • Side B: 2
  • Side C: 5
  • Result: Cannot form a triangle with these side lengths (Triangle Inequality Theorem violated).

This calculator is a handy tool for students, educators, and anyone needing quick and accurate triangle property analysis based on side lengths.

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