Pada △ABC diketahui panjang sisi a=7 cm, b=8 cm, c=9 cm. Tentukan panjang besar sudut ∠A, ∠B, ∠C!

Pertanyaan

Pada $\bigtriangleup\mathrm{ABC}$ diketahui panjang sisi $a=7\;\mathrm{cm},\;b=8\;\mathrm{cm},\;c=9\;\mathrm{cm}$ . Tentukan panjang besar sudut $\angle A,\;\angle B,\;\angle C$ !

A. Fatta

Master Teacher

Mahasiswa/Alumni Institut Pertanian Bogor

Jawaban terverifikasi

Pembahasan

Aturan Cosinus merupakan aturan yang menjelaskan hubungan antara kuadrat panjang sisi dengan nilai cosinus dari salah satu sudut pada segitiga. Aturan cosinus dapat digunakan untuk menentukan unsur-unsur lain dalam suatu segitiga sembarang untuk dua kasus yaitu saat tiga sisi ketahui dan saat dua sisi dan sudut apitnya diketahui.

Rumus untuk menghitung besar sudut pada triangle ABC sebagai berikut :

$table attributes columnalign right center left columnspacing 0px end attributes row cell cos space A end cell equals cell fraction numerator b squared plus c squared minus a squared space over denominator 2 b c end fraction end cell row cell cos space B end cell equals cell fraction numerator c squared plus a squared minus b squared space over denominator 2 a c end fraction end cell row cell cos space C end cell equals cell fraction numerator a squared plus b squared minus c squared space over denominator 2 a b end fraction end cell end table$

Diketahui panjang sisi a equals 7 space cm comma space b equals 8 space cm comma space c equals 9 space cm .

Akan diperoleh angle A sebagai berikut:

$table attributes columnalign right center left columnspacing 0px end attributes row cell cos space A end cell equals cell fraction numerator b squared plus c squared minus a squared space over denominator 2 b c end fraction end cell row blank equals cell fraction numerator 8 squared plus 9 squared minus 7 squared over denominator 2 cross times 8 cross times 9 end fraction end cell row blank equals cell fraction numerator 64 plus 81 minus 49 over denominator 144 end fraction end cell row blank equals cell 96 over 144 end cell row blank equals cell 2 over 3 end cell row cell angle A end cell equals cell cos to the power of negative 1 end exponent open parentheses 2 over 3 close parentheses end cell row cell angle A end cell equals cell 48 comma 19 degree end cell end table$

Akan diperoleh angle B sebagai berikut:

$table attributes columnalign right center left columnspacing 0px end attributes row cell cos space B end cell equals cell fraction numerator c squared plus a squared minus b squared space over denominator 2 a c end fraction end cell row blank equals cell fraction numerator 9 squared plus 7 squared minus 8 squared space over denominator 2 cross times 7 cross times 9 end fraction end cell row blank equals cell fraction numerator 81 plus 49 minus 64 over denominator 126 end fraction end cell row blank equals cell 66 over 126 end cell row blank equals cell 11 over 21 end cell row cell angle B end cell equals cell cos to the power of negative 1 end exponent open parentheses 11 over 21 close parentheses end cell row cell angle B end cell equals cell 58 comma 41 degree end cell end table$

Akan diperoleh angle C sebagai berikut:

$table attributes columnalign right center left columnspacing 0px end attributes row cell cos space C end cell equals cell fraction numerator a squared plus b squared minus c squared space over denominator 2 a b end fraction end cell row blank equals cell fraction numerator 7 squared plus 8 squared minus 9 squared space over denominator 2 cross times 7 cross times 8 end fraction end cell row blank equals cell fraction numerator 49 plus 64 minus 81 over denominator 112 end fraction end cell row blank equals cell 32 over 112 end cell row blank equals cell 2 over 7 end cell row cell angle C end cell equals cell cos to the power of negative 1 end exponent open parentheses 2 over 7 close parentheses end cell row cell angle C end cell equals cell 73 comma 4 degree end cell end table$

Dengan demikian, diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell angle A end cell equals cell 48 comma 19 degree end cell row cell angle B end cell equals cell 58 comma 41 degree end cell row cell angle C end cell equals cell 73 comma 4 degree end cell end table

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