Krishna
0

Step 1:  Recall the cosines formula

            The law of cosines is a formula that relates the three sides of a triangle to

            the cosine of a given angle

                                

              FORMULA:   a^2 = b^2 + c^2 - 2bc \cos(A)

                                     b^2 = a^2 + c^2 - 2ac \cos(B)

                                     c^2 = b^2 + a^2 - 2ba \cos(C)


              Where each lowercase letter (like a) is the length of the side opposite the

              vertex labeled with the same capital letter.


Step 2: Use the cosine formula to find unknown length.

                Since you know

                      The lengths of two sides f = 6

                                                            h = 12

              The measure of the included angle \angle FGH = 46\degree

                              Unknown length  g = ?

                    Cosines formula

                                   g^2 = h^2 + f^2 - 2fh \cos 46\degree

                                   g^2 = 12^2 + 6^2 - 2(6*12) \cos 46\degree

                                   g^2 = 144 + 36 - 144 (0.694)       (\because use\ calculator\ to\ find\ the\cos46\degree\ value)

                                     g^2 = 79.969   

                                     g =8.942