Law of Cosines Calculator

- May 09, 2025
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Calculate missing sides or angles in a triangle using the Law of Cosines. This calculator helps solve triangles when you know three pieces of information about a triangle.

Triangle Input

a b c A B C
units
units
units
°
°
°

Display Options

About the Law of Cosines

The Law of Cosines is a fundamental formula in trigonometry that relates the sides and angles of a triangle. It's a generalisation of the Pythagorean theorem to any triangle, not just right triangles.

When to Use the Law of Cosines
  • SAS (Side-Angle-Side): When you know two sides and the included angle
  • SSS (Side-Side-Side): When you know all three sides
  • SSA (Side-Side-Angle): When you know two sides and a non-included angle (may have 0, 1, or 2 solutions)
Applications

The Law of Cosines is used in various fields including:

  • Surveying and navigation
  • Engineering and construction
  • Physics and vector analysis
  • Astronomy for calculating distances between celestial objects
  • Computer graphics for 3D modelling

Understanding the Law of Cosines Calculator

The Law of Cosines Calculator is a handy tool that helps you solve triangles. If you know certain parts of a triangle, like sides or angles, this calculator can find the missing pieces. It’s especially useful for triangles that don’t have a right angle. With just a few inputs, you can get the results you need quickly and accurately.

How to Use the Calculator

Using the Law of Cosines Calculator is straightforward. You can choose to find either sides or angles based on the information you have. Simply input the lengths of the sides or the angles as required. The calculator then performs the necessary calculations and displays the result, allowing you to see the full triangle's details.

Input Options for Your Triangle

  • Sides: You can enter the lengths of two sides and the included angle (SAS) or all three sides (SSS).
  • Angles: If you prefer, you can provide two sides and a non-included angle (SSA) to find the remaining angle.

Features of the Law of Cosines Calculator

This calculator comes with several useful features. You can adjust the number of decimal places in the results, choose between degrees and radians for angles, and even see step-by-step calculations. These options help ensure that you get the exact information you need, presented in a way that’s easy to understand.

Why Use the Law of Cosines?

The Law of Cosines is a vital formula in trigonometry. It allows you to relate the lengths of the sides of a triangle to its angles. This is not just for right triangles; it works for all types of triangles. Knowing when and how to use this law can simplify many problems in Geometry and real-world applications.

Applications of the Law of Cosines

  • Surveying: Measuring land and properties.
  • Engineering: Designing structures and systems.
  • Astronomy: Calculating distances in space.

Understanding Triangle Properties

Besides finding sides and angles, this calculator also provides additional information about the triangle. It can calculate the area, perimeter, and the type of triangle based on the side lengths. This extra data can be useful in many fields, including architecture, construction, and design.

Getting the Most from Your Calculator

To make the most of the Law of Cosines Calculator, it’s helpful to have a clear understanding of your triangle's properties. Knowing what information you have and what you need to find will streamline your calculations. Whether you’re working on homework, a project, or a practical application, this tool can make your task much easier.