Law of Cosines Calculator



Welcome to our insightful exploration of the Law of Cosines, a cornerstone concept in engineering and mathematics. This page is tailored for engineering enthusiasts and professionals who are eager to deepen their understanding of this fundamental theorem. Whether you’re solving complex engineering problems or just satisfying your curiosity about geometric principles, our clear and concise guide will provide you with the knowledge you need.

What is Law of Cosines?

The Law of Cosines is a critical theorem in trigonometry that relates the lengths of the sides of a triangle to the cosine of one of its angles. This principle is not just a theoretical construct; it’s a practical tool used extensively in various fields of engineering, including mechanical, civil, and aerospace engineering. This law becomes particularly useful in solving triangles when the standard right-angle trigonometric ratios do not apply, making it a versatile solution in non-right triangles.

Law of Cosines Calculator

\( c^2 = a^2 + b^2 – 2ab \cos(C) \)


  • a, b – Lengths of the sides of the triangle,
  • c – Length of the side opposite angle C,
  • C – Angle opposite side c.

Law of Cosines is a fundamental theorem in trigonometry used for calculating unknown parts of a triangle, especially in non-right angled triangles. It’s essential in fields like engineering, physics, and geometry for accurate measurement and problem-solving.

Frequently Asked Questions

Q: How is the Law of Cosines applied in real-world engineering?
A: In engineering, the Law of Cosines is used in fields such as structural analysis, mechanical design, and navigation. For instance, it helps in determining the forces acting on non-perpendicular components in structures or machinery.

Q: Can the Law of Cosines be used for all types of triangles?
A: Yes, the Law of Cosines is applicable to all types of triangles, whether they are acute, obtuse, or right-angled. This universality makes it a valuable tool in engineering calculations.

Q: How does the Law of Cosines differ from the Law of Sines?
A: While both laws are used for solving triangles, the Law of Cosines is particularly useful for calculating a side length or an angle when two sides and the included angle, or all three sides, are known. The Law of Sines, on the other hand, is more applicable when dealing with two angles and a side or two sides and a non-included angle.

Q: Are there any limitations to using the Law of Cosines?
A: The primary limitation of the Law of Cosines arises in computational scenarios, where calculating the cosine of very small or very large angles can lead to errors due to rounding in digital computations. However, in practical engineering applications, these limitations are well-understood and managed.