The Law of Cosines


     


For solving a triangle,
    the two cases

     1]  Two sides and the included angle (SAS) are given
                    or
     2]  Three sides (SSS) are given

cannot be solved using the law of sines.

Both cases can be solved using the

                                                  Law of Cosines

                                                  In any triangle
          

     
     
     


These three equations say the same thing
They express the same relationship that exists
among the three sides and corresponding angles of a triangle
In words, the square of any side is equal to the sum of the squares
of the remaining two sides diminished by twice the product of the two sides
and the cosine of the included angle

In practice, when solving a triangle, the law of cosines and the law of sines
may both be used in combination

Solving the SAS Case –
                                       see Example 1, pages 590 – 591, and Example 3, page 593, of the textbook

Solving the SSS case –
                                     see Example 2, pages 592 – 593, of the textbook


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