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Pertanyaan

Diketahui AB with rightwards arrow on top equals open parentheses table row cell negative 2 end cell row cell negative 4 end cell row 2 end table close parentheses dan BC with rightwards arrow on top equals open parentheses table row 2 row 1 row 1 end table close parentheses. Tentukan besar sudut BAC

L. Rante

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Jawaban

besar sudut BAC adalah 30 degree.  

Pembahasan

Diketahui AB with rightwards arrow on top equals open parentheses table row cell negative 2 end cell row cell negative 4 end cell row 2 end table close parentheses dan BC with rightwards arrow on top equals open parentheses table row 2 row 1 row 1 end table close parentheses, maka 

table attributes columnalign right center left columnspacing 0px end attributes row cell AC with rightwards arrow on top end cell equals cell AB with rightwards arrow on top plus BC with rightwards arrow on top end cell row blank equals cell open parentheses table row cell negative 2 end cell row cell negative 4 end cell row 2 end table close parentheses plus open parentheses table row 2 row 1 row 1 end table close parentheses end cell row blank equals cell open parentheses table row 0 row cell negative 3 end cell row 3 end table close parentheses end cell end table  

Sudut BAC adalah sudut antara AB with rightwards arrow on top dengan AC with rightwards arrow on top . Misalnya sudut tersebut adalah theta, maka 

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space straight theta end cell equals cell fraction numerator AB with rightwards arrow on top times stack A C with rightwards arrow on top over denominator open vertical bar AB with rightwards arrow on top close vertical bar times open vertical bar stack A C with rightwards arrow on top close vertical bar end fraction end cell row blank equals cell fraction numerator open parentheses table row cell negative 2 end cell row cell negative 4 end cell row 2 end table close parentheses times open parentheses table row 0 row cell negative 3 end cell row 3 end table close parentheses over denominator square root of open parentheses negative 2 close parentheses squared plus open parentheses negative 4 close parentheses squared plus open parentheses 2 close parentheses squared end root times square root of 0 squared plus open parentheses negative 3 close parentheses squared plus 3 squared end root end fraction end cell row blank equals cell fraction numerator 0 plus 12 plus 6 over denominator square root of 24 times square root of 18 end fraction end cell row blank equals cell fraction numerator 18 over denominator square root of 432 end fraction end cell row blank equals cell fraction numerator 18 over denominator 12 square root of 3 end fraction end cell row blank equals cell fraction numerator 3 over denominator 2 square root of 3 end fraction end cell row blank equals cell 1 half square root of 3 end cell end table 

Sehingga 

theta equals cos to the power of negative 1 end exponent open parentheses 1 half square root of 3 close parentheses equals 30 degree 

Jadi, besar sudut BAC adalah 30 degree.  

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