Pertanyaan

Jika panjang BC = 10 cm, maka panjang AB = … cm

Jika panjang BC = 10 cm, maka panjang AB = $\dots$ cm

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

Pembahasan

Ingat bahwa pada segitiga siku-siku, . Perhatikan segitiga siku-siku BCD! Perhatikan segitiga siku-siku ACD! Jadi, jawaban yang tepat adalah E.

Ingat bahwa pada segitiga siku-siku, tan space straight x equals depan over samping .

Perhatikan segitiga siku-siku BCD!

table attributes columnalign right center left columnspacing 0px end attributes row cell tan space straight B end cell equals cell CD over BC end cell row cell tan space 45 degree end cell equals cell CD over 10 end cell row 1 equals cell CD over 10 end cell row CD equals cell 10 space cm end cell end table

Perhatikan segitiga siku-siku ACD!

$table attributes columnalign right center left columnspacing 0px end attributes row cell tan space straight A end cell equals cell CD over AC end cell row cell tan space 30 degree end cell equals cell fraction numerator 10 over denominator AB plus BC end fraction end cell row cell fraction numerator square root of 3 over denominator 3 end fraction end cell equals cell fraction numerator 10 over denominator AB plus 10 end fraction end cell row cell square root of 3 open parentheses AB plus 10 close parentheses end cell equals cell 3 times 10 end cell row cell square root of 3 AB plus 10 square root of 3 end cell equals 30 row cell square root of 3 AB end cell equals cell 30 minus 10 square root of 3 end cell row AB equals cell fraction numerator 30 minus 10 square root of 3 over denominator square root of 3 end fraction end cell row AB equals cell fraction numerator 30 minus 10 square root of 3 over denominator square root of 3 end fraction times fraction numerator square root of 3 over denominator square root of 3 end fraction end cell row AB equals cell fraction numerator square root of 3 over denominator 3 end fraction open parentheses 30 minus 10 square root of 3 close parentheses end cell row AB equals cell 1 third open parentheses 30 square root of 3 minus 30 close parentheses end cell row AB equals cell 1 third times 30 open parentheses square root of 3 minus 1 close parentheses end cell row AB equals cell 10 open parentheses square root of 3 minus 1 close parentheses space cm end cell end table$

Jadi, jawaban yang tepat adalah E.