Law of Cosines Calculator

- May 09, 2025
| |

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

The Law of Cosines is a key formula in trigonometry. It helps you figure out the sides and angles of a triangle. This law extends the Pythagorean theorem, making it useful for any triangle, not just right ones. It is particularly handy when you know two sides and the included angle or all three sides. When using this law, you can solve for unknown lengths or angles efficiently.

Introducing the Law of Cosines Calculator

The Law of Cosines Calculator is a valuable tool for anyone working with triangles. It allows you to calculate missing sides or angles easily. Enter the information you have, like two sides and the included angle, or all three sides. The calculator then gives you the results in a matter of moments, saving you time on complex calculations.

How to Input Triangle Data

When using this calculator, you can choose to find a side or an angle. To do this, you'll enter the values of the sides or angles you know. The calculator has designated areas for side lengths (a, b, c) and angle measures (A, B, C). By selecting the appropriate mode—whether for sides or angles—you can tailor your inputs to suit your needs.

Key Features of the Calculator

  • Calculate side lengths using SAS or SSS configurations.
  • Determine angle measures with SSA setup.
  • Visual representations of triangles for better understanding.
  • Options to display calculation steps for transparency.

Adjustable Settings for Your Needs

The calculator offers adjustable settings to enhance your experience. You can select the number of decimal places for your results, ensuring accuracy as needed. Additionally, you can choose whether to see the calculation steps. This way, you can follow along with the process and understand how the results are derived.

Applications in Real Life

The Law of Cosines Calculator is not only useful for students but also for professionals in various fields. It is commonly applied in areas such as:

  • Surveying and navigation, where precise measurements are critical.
  • Engineering and construction for designing structures.
  • Physics for solving problems involving vectors.
  • Astronomy for calculating distances between celestial bodies.

Understanding Triangle Properties

After using the calculator, you’ll gain insights into important triangle properties. It can calculate the area, perimeter, and type of triangle based on the sides you input. This information is useful for recognising the characteristics of the triangle you are working with. For example, knowing whether a triangle is scalene or isosceles can influence design choices in engineering and architecture.

Final Thoughts on Using the Law of Cosines Calculator

This calculator simplifies the process of solving triangles and is an essential resource for anyone dealing with Geometry. Whether you are a student learning the fundamentals or a professional needing quick calculations, this tool can make your tasks easier. Understanding the Law of Cosines and utilising this calculator can greatly improve your efficiency in solving triangle-related problems.