Pada segitiga ABC, s=6, s−a=3, s−b=2, dan s−c=1 dengan s=21× keliling △ ABC. Nilai cos A adalah ....

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Pada segitiga ABC, $\style{font-size:14px}{s=6}$ , $\style{font-size:14px}{s-a=3}$ , $\style{font-size:14px}{s-b=2}$ , dan $\style{font-size:14px}{s-c=1}$ dengan $\style{font-size:14px}{s=\frac12\times}$ keliling $\style{font-size:14px}\bigtriangleup$ ABC. Nilai $\style{font-size:14px}{\cos\;\mathrm A}$ adalah ....

F. Ayudhita

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Jika diketahui ,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell s minus a end cell equals 3 row cell 6 minus a end cell equals 3 row a equals 3 end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell s minus b end cell equals 2 row cell 6 minus b end cell equals 2 row b equals 4 end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell s minus c end cell equals 1 row cell 6 minus c end cell equals 1 row c equals 5 end table end style

Gunakan aturan cos untuk mengetahui nilai

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cos space A end cell equals cell fraction numerator b squared plus c squared minus a squared over denominator 2 b c end fraction end cell row blank equals cell fraction numerator 4 squared plus 5 squared minus 3 squared over denominator 2 times 4 times 5 end fraction end cell row blank equals cell fraction numerator 16 plus 25 minus 9 over denominator 40 end fraction end cell row blank equals cell 32 over 40 end cell row blank equals cell 4 over 5 end cell end table end style$

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