Law of Cosines Calculator: Find Angles & Sides
Easily calculate unknown sides or angles of a triangle using the Law of Cosines. Enter known values and get instant results with visualization.
Understanding the Law of Cosines
The Law of Cosines relates the sides and angles of a triangle. It's particularly useful for solving triangles when you know:
- Two sides and the included angle (SAS).
- All three sides (SSS).
Use this calculator to find unknown sides or angles by inputting the known values. Select what you want to calculate (unknown) and enter the rest of the values.
Triangle Visualization
Law of Cosines: Quick Guide
The Law of Cosines is a fundamental theorem in trigonometry that generalizes the Pythagorean theorem. It states that in any triangle, the square of the length of one side is equal to the sum of the squares of the lengths of the other two sides minus twice the product of their lengths and the cosine of the angle included between the other two sides.
It is expressed by the formula: where \'a\', \'b\', and \'c\' are the lengths of the sides of the triangle, and 'C' is the angle opposite side \'c\'. This law is essential for solving triangles when you don\'t have a right angle, especially in cases of Side-Angle-Side (SAS) and Side-Side-Side (SSS) scenarios. It helps in finding unknown sides or angles, making it a versatile tool in geometry, physics, and engineering.
For further reading and more complex applications, you can refer to resources like: