CBSE Class 11-science Answered

In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of an arbitrary triangle to the sines of its angles. According to the law,

where a, b, and c are the lengths of the sides of a triangle, and A, B, and C are the opposite angles (see the figure to the right), and D is the diameter of the triangle's circumcircle. 

In trigonometry, the law of cosines (also known as the cosine formula or cosine rule) relates the lengths of the sides of a planetriangle to the cosine of one of its angles. 

where ? denotes the angle contained between sides of lengths a and b and opposite the side of length c.

By changing which sides of the triangle play the roles of a, b, and c in the original formula, one discovers that the following two formulas also state the law of cosines:

Where alpha and beta are the angles between sides b and c and sides a and c respectively.