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Diketahui perbandingan panjang sisi-sisi segitiga ...

Diketahui perbandingan panjang sisi-sisi segitiga undefined adalah begin mathsize 14px style 2 colon 6 colon 7 end style. Nilai cosinus sudut terbesar adalah ....

  1. begin mathsize 14px style.... end style  

  2. undefined 

Jawaban:

Misal, isi-sisi segitga ABC yaitu begin mathsize 14px style AB equals 2 straight x comma space BC equals 6 straight x comma space AC equals 7 straight x end style.

Sudut terbesar terletak di depan sisi terpanjang. Jika sisi terpanjang AC, maka sudut terbesar adalah B. Sehingga:

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell AC squared end cell equals cell AB squared plus BC squared minus 2 open parentheses AB close parentheses open parentheses BC close parentheses space cos space angle straight A end cell row cell open parentheses 7 straight x close parentheses squared end cell equals cell open parentheses 2 straight x close parentheses squared plus open parentheses 6 straight x close parentheses squared minus 2 open parentheses 2 straight x close parentheses open parentheses 6 straight x close parentheses space cos space angle straight A end cell row cell 49 straight x squared end cell equals cell 4 straight x squared plus 36 straight x squared minus 24 straight x squared space cos space angle straight A end cell row cell 49 straight x squared end cell equals cell 40 straight x squared minus 24 straight x squared space cos space angle straight A end cell row cell 9 straight x squared end cell equals cell 24 straight x squared space cos space angle straight A end cell row cell cos space angle straight A end cell equals cell 9 over 24 end cell row cell cos space angle straight A end cell equals cell 3 over 8 end cell end table end style 

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