Triangle Sides Calculator

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Triangle Sides Calculator

Calculate the length of the third side using the Law of Cosines (SAS – Side Angle Side).

The angle between Side A and Side B.

Calculation Results:

Side C Length:

Triangle Perimeter:

Triangle Area:

function calculateTriangleSide() { var a = parseFloat(document.getElementById('sideA').value); var b = parseFloat(document.getElementById('sideB').value); var angleDeg = parseFloat(document.getElementById('angleC').value); var resultDiv = document.getElementById('triangleResult'); if (isNaN(a) || isNaN(b) || isNaN(angleDeg) || a <= 0 || b <= 0 || angleDeg = 180) { alert("Please enter valid positive numbers. Note: The angle must be between 0 and 180 degrees."); return; } // Convert angle to radians var angleRad = angleDeg * (Math.PI / 180); // Law of Cosines: c^2 = a^2 + b^2 – 2ab * cos(C) var cSquared = (a * a) + (b * b) – (2 * a * b * Math.cos(angleRad)); var c = Math.sqrt(cSquared); // Calculate Perimeter var perimeter = a + b + c; // Calculate Area using Sine: Area = 0.5 * a * b * sin(C) var area = 0.5 * a * b * Math.sin(angleRad); // Display Results document.getElementById('resSideC').innerText = c.toFixed(4); document.getElementById('resPerimeter').innerText = perimeter.toFixed(4); document.getElementById('resArea').innerText = area.toFixed(4); resultDiv.style.display = 'block'; }

Understanding the Triangle Sides Calculator

Finding the missing side of a triangle is a fundamental task in geometry, trigonometry, and various engineering fields. This calculator utilizes the Law of Cosines to determine the length of the third side when you know the lengths of two sides and the measure of the angle between them (known as the Side-Angle-Side or SAS configuration).

The Law of Cosines Formula

The Law of Cosines is a generalization of the Pythagorean theorem. While the Pythagorean theorem only works for right-angled triangles, the Law of Cosines works for any triangle. The formula is expressed as:

c² = a² + b² – 2ab * cos(γ)
  • a and b: The lengths of the two known sides.
  • γ (gamma): The included angle between sides a and b.
  • c: The length of the unknown third side.

Practical Examples

Example 1: The Right Triangle
Suppose you have a right triangle where Side A is 3 units and Side B is 4 units. Since it is a right triangle, the included angle is 90 degrees.
Calculation: c² = 3² + 4² – 2(3)(4) * cos(90°). Since cos(90°) = 0, the formula simplifies to 9^ + 16 = 25. Therefore, Side C = 5.

Example 2: The Obtuse Triangle
Imagine a triangle where Side A is 10, Side B is 15, and the angle between them is 120 degrees.
Calculation: c² = 10² + 15² – 2(10)(15) * cos(120°). Since cos(120°) = -0.5, the formula becomes c² = 100 + 225 – (300 * -0.5) = 325 + 150 = 475. Side C is approximately 21.79.

Why Use This Calculator?

Manually calculating triangle sides involves converting degrees to radians and performing square root operations which are prone to human error. This tool is essential for:

  • Construction: Determining roof pitches or bracing lengths.
  • Navigation: Calculating the distance between two points given a specific heading.
  • Education: Checking homework answers in trigonometry and geometry classes.
  • DIY Projects: Building furniture or frames where precise angles are required.

Frequently Asked Questions

What if I only know the angles?
If you only know the angles and no side lengths, the size of the triangle cannot be determined (it could be any size). You need at least one side length to find others using the Law of Sines.

Can the angle be 180 degrees?
No. In a triangle, the sum of all internal angles must be 180 degrees. A single angle of 180 degrees would result in a straight line, not a triangle.

Does this work for equilateral triangles?
Yes. In an equilateral triangle, all sides are equal and all angles are 60 degrees. If you input Side A = 10, Side B = 10, and Angle = 60, the result for Side C will be 10.

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