Law of Cosines

                     Lesson 1

                                                                                                                                                                          

                                                            Problem:   In ∆RST, side s = 16, side t = 14 and m<R = 65. Find side r to the nearest integer.     

                                                                                               

                                                            

                                                            Solution     This problem involves all three sides but only one angle of

Step 1: the triangle. This fits the profile for the Law of Cosines.

r2 = s2 +t2 2st Cos x                                                                             

                     

                                                            Solution       r2 = 162 + 142 2 * 16 * 14 * cos65

Step 2:           r2 = 256 + 196 179.2            

                                                                                         

                                                            Solution     x2 = 272.8  

Step 3:                        

 

                                                            Solution      x = 16.5

Step 4:      

 

Solution      Answer: 16.5

Step 5:                                               

Complete                                                                   

                                                                                                                               

                                                             Try two practice problems:  

 

                                                                                 Solve the following:

 

A.

In ∆ASD, m<S = 78,

a = 13 and s = 41. Find the length of side d, to the nearest integer.

B.

In a rhombus whose side measures 60 and the smaller angle is 36; find the length of the larger diagonal, to the nearest tenth.

 

 

 

 

 

 

        

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