Law of Sines

The law of sines, also known as the sine rule, is a mathematical relationship that relates the lengths of the sides of a triangle to the sines of its angles. It can be used to solve triangles that are not right angled.  In other words, the ratio of the length of a side of a triangle to the sine of the angle opposite to that side is the same for all sides and angles of the triangle.

The law of sines is useful when you know the lengths of one side and its opposite angle, or when you know the lengths of two sides and their included angle, and need to find the length of another side or the measure of another angle.

The law of sines is widely used in trigonometry, geometry, navigation, and other fields where triangle relationships and measurements are involved.

 

Law of Sines Formulas

\( sinA\;/\;a = sinB\;/\;b = sinC\;/\;c\) or three separate equations: \( sinA\;/\;a = sinB\;/\;b\) \( sinA\;/\;a = sinC\;/\;c\) \( sinB\;/\;b = sinC\;/\;c\)