Respostas
Fórmulas para encontrar ângulos de A, B e C:
αa = arc cos a2 – b2 – c2 / – 2.b.c
αb = arc cos b2 – a2 – c2 / – 2.a.c
αc = arc cos c2 – a2 – b2 / – 2.a.b
-Resposta:
αa = arc cos a2 – b2 – c2 / – 2.b.c
αa = arc cos (21)2 – (19,5)2 – (22)2 / – 2.(19,5).(22)
αa = arc cos (441) – (380,25) –(484) / – 2.(19,5).(22)
αa = arc cos 0,493298368
αa = 60º26’32”
αb = arc cos b2 – a2 – c2 / – 2.a.c
αb = arc cos (19,5)2 – (21)2 –(22)2 / – 2.(21).(22)
αb = arc cos (380) – (441) – (484) / – 2.(21).(22)
αb = arc cos 0,589826839
explicação
αb = 53º51’19”
αc = arc cos c2 – a2 – b2 / – 2.a.b
αc = arc cos (22)2 – (21)2 – (19,5)2 / – 2.(21).(19,5)
αc = arc cos (484) – (441) – (380,25) /- 2.(21).(19,5)
αc = arc cos 0411782661
αc = 65º40’59”
Verificação:
Σαi = 180º
Σαi = αa + αb + αc = 60º26’32” + 53º51’19” + 65º40’59” = 179º58’50”