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

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Bria Mccoy · Accepted Answer

Solve the measure of sides a, b and c respectively.  a  =      |    B  C      |      =      (    1    −    2          )      2        +    (    −    2    −    1          )      2          =      10  Similiarly,  b  =      (    −    1    −    1          )      2        +    (    0    −    (    −    2    )          )      2          =  2      2      c  =      (    2    −    (    −    1    )          )      2        +    (    1    −    0          )      2          =      10  Now, using cosine formula,  cos  ⁡  (  A  )  =            (      2              2                    )        2            +      (              10                    )        2            −      (              10                    )        2                    2      (      2              2            )      (              10            )          =      1          5          A  =      cos          −      1        ⁡  (            5        5    )Similarly, angles B and C can be calculated as  cos  ⁡  (  B  )  =            (              10                    )        2            +      (              10                    )        2            −      (      2              2                    )        2                    (      2              10            )      (              10            )          =      12    20      B  =      cos          −      1        ⁡  (      3    5    )    cos  ⁡  (  C  )  =            (              10                    )        2            +      (      2              2                    )        2            −      (              10                    )        2                    (      2      (              10            )      (      2              2            )          =      1          5          C  =      cos          −      1        ⁡  (            5        5    )

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

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