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Pertanyaan

Diketahul segitiga ABC comma space AC equals 6 comma space BC equals 5 comma space dan space angle straight A equals 30 degree comma space maka space nilai space tan space straight B adalah...

Z. Apriani

Master Teacher

Mahasiswa/Alumni Institut Pertanian Bogor

Jawaban terverifikasi

Pembahasan

Dengan menggunakan aturan sinus diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator AC over denominator sin space straight B end fraction end cell equals cell fraction numerator BC over denominator sin space straight A end fraction end cell row cell fraction numerator 6 over denominator sin space straight B end fraction end cell equals cell fraction numerator 5 over denominator sin space 30 degree end fraction end cell row cell sin space straight B end cell equals cell 1 half cross times 6 over 5 end cell row blank equals cell 6 over 10 end cell row blank equals cell 3 over 5 end cell end table

Sehingga,

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space straight B end cell equals cell square root of 1 minus sin squared straight B end root end cell row blank equals cell square root of 1 minus open parentheses 3 over 5 close parentheses squared end root end cell row blank equals cell square root of 25 over 25 minus 9 over 25 end root end cell row blank equals cell square root of 16 over 25 end root end cell row blank equals cell 4 over 5 end cell end table

Jadi,

table attributes columnalign right center left columnspacing 0px end attributes row cell tan space straight B end cell equals cell fraction numerator sin space straight B over denominator cos space straight B end fraction end cell row blank equals cell fraction numerator begin display style 3 over 5 end style over denominator begin display style 4 over 5 end style end fraction end cell row blank equals cell 3 over 5 cross times 5 over 4 end cell row blank equals cell 3 over 4 end cell end table

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