# The Sine Rule

Let us now look at the Sine Rule

Objectives
 At the end of this session we should be able to state the sine rule apply Sine Rule to calculate the lengths of sides of an angle apply Sine Rule to calculate the sizes of angles apply Sine Rule to solve word problems

The law of sines (sines law, sine formula, sine rule), in trigonometry, is a statement about any triangle in a plane. Where the sides of the triangle are a, b and c and the angles opposite those sides are A, B and C, then the law of sines states:

$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} =$

where R is the radius of the triangle's circumcircle. This law is useful when computing the remaining sides of a triangle if two angles and a side are known, a common problem in the technique of triangulation. It can also be used when two sides and one of the non-enclosed angles are known; in this case, the formula may give two possible values for the enclosed angle. When this happens, often only one result will cause all angles to be less than 180°; in other cases, there are two valid solutions to the triangle