Mastering the Law of Sines and Law of Cosines Calculator

Trigonometry allows us to solve for unknown sides and angles in any triangle, not just right-angled ones. Two powerful rules govern these oblique triangles: the Law of Sines and the Law of Cosines. This tool applies the correct formula based on the information you have available.

When to use the Law of Sines

The Law of Sines states that the ratio of the length of a side to the sine of its opposite angle is constant for all three sides.
a / sin A = b / sin B = c / sin C
Use this law when you know:

• ASA: Two angles and the included side.
• AAS: Two angles and a non-included side.
• SSA: Two sides and a non-included angle (The Ambiguous Case).

When to use the Law of Cosines

The Law of Cosines is a generalization of the Pythagorean Theorem. It relates the lengths of sides to the cosine of one of its angles.
c² = a² + b² – 2ab cos(C)
Use this law when you know:

• SSS: All three sides.
• SAS: Two sides and the angle between them.

Why use a Law of Sines and Law of Cosines Calculator?

Solving these equations manually involves multiple steps of algebra and inverse trigonometric functions, which introduces many opportunities for rounding errors or sign mistakes. This calculator automates the process, ensuring precision, and provides a visual verification that the calculated triangle is geometrically possible.