Trigonometry

Study of triangles and trigonometric functions including sine, cosine, and tangent.

Advanced Topics

Solving Triangles: The Laws of Sines and Cosines

Laws for Any Triangle

Not all triangles are right triangles! The Law of Sines and Law of Cosines let you solve for unknown sides or angles in any triangle.

Law of Sines

\[ \frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)} \]

Law of Cosines

\[ c^2 = a^2 + b^2 - 2ab\cos(C) \]

These laws are powerful tools for solving triangles when you have limited information.

When to Use Each Law

  • Use the Law of Sines when you have an angle and its opposite side.
  • Use the Law of Cosines for finding a side when you know two sides and the included angle.

Examples

  • Finding the distance between two cities using the Law of Cosines.

  • Determining an unknown angle in a scalene triangle with the Law of Sines.

In a Nutshell

The Laws of Sines and Cosines help solve for unknowns in any triangle, not just right triangles.

Solving Triangles: The Laws of Sines and Cosines - Trigonometry Content | Practice Hub