Find the measures of the angles of the triangle whose vertices are A = (-1,0), B = (2,1), C = (1,-2).

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Jaxson White · Accepted Answer

A      B        ¯    =      (    −    1    −    2          )              2              +    (    0    −    1          )              2              =      9    +    1    =      10              B      C        ¯    =      (    1    −    2          )              2              +    (    −    2    −    1          )              2              =      1    +    9    =      10              A      C        ¯    =      (    −    1    −    1          )              2              +    (    0    +    2          )              2              =      4    +    4    =  2      2  we will use      a          2        =      b          2        +      c          2        −  2  b  c  cos  ⁡  (  θ  ) where   θ is angle Awe have:  cos  ⁡  (  ∠  A  B  C  )  =                              A                      B                          2                                      ¯            +                        B                      C                          2                                      ¯            −                        A                      C                          2                                      ¯                    2      ∗                        B                      C                          2                                      ¯            ∗                        A                      B                          2                                      ¯              =            10      +      10      −      8              2      ∗              10            ∗              10              =      12    20    =      3    5    ∠  A  B  C  =      cos          −      1        ⁡  (      3    5    )  =      53.13          0        cos  ⁡  (  ∠  A  C  B  )  =            (      B      C              )                  2                    +      (      A      C              )                  2                    −      (      A      B              )                  2                            2      ∗      B      C      ∗      A      C        =            10      +      8      −      10              2      ∗              10            ∗              8              =      8          2              80              =      4          4              5              =            5        5    ∠  B  A  C  =      63.43          0

Find the measures of the angles of the triangle whose vertices are A = (-1,0), B = (2,1), C = (1,-2).

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