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Diketahui segitiga ABC; CD tegak lurus AD. AD=10, BD=3 dan sin A=0,2. Tentukanlah nilai tan C.

Pertanyaan

Diketahui segitiga ABC; CD tegak lurus AD. AD equals 10BD equals 3 dan sin space A equals 0 comma 2. Tentukanlah nilai tan space C.

R. Hajrianti

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

nilai tan space C adalah 2 square root of 6.

Pembahasan

Diketahui:

Segitiga ABC; CD tegak lurus AD. AD equals 10BD equals 3, digambarkan sebagai berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space A end cell equals cell 0 comma 2 end cell row cell CD over AC end cell equals cell 2 over 10 end cell end table

Dengan menggunakan Teorema Pythagoras, diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell AC squared end cell equals cell CD squared plus AD squared end cell row cell open parentheses 10 x close parentheses squared end cell equals cell open parentheses 2 x close parentheses squared plus 10 squared end cell row cell 100 x squared end cell equals cell 4 x squared plus 100 end cell row cell 100 x squared minus 4 x squared end cell equals 100 row cell 96 x squared end cell equals 100 row cell x squared end cell equals cell 100 over 96 end cell row cell x squared end cell equals cell 25 over 24 end cell row x equals cell square root of 25 over 24 end root end cell row x equals cell fraction numerator 5 over denominator square root of 24 end fraction end cell row x equals cell fraction numerator 5 over denominator 2 square root of 6 end fraction times fraction numerator square root of 6 over denominator square root of 6 end fraction end cell row x equals cell fraction numerator 5 square root of 6 over denominator 2 times 6 end fraction end cell row x equals cell 5 over 12 square root of 6 end cell end table

Akibatnya:

table attributes columnalign right center left columnspacing 0px end attributes row CD equals cell 2 x end cell row blank equals cell 2 open parentheses 5 over 12 square root of 6 close parentheses end cell row blank equals cell 5 over 6 square root of 6 end cell row blank blank blank row AC equals cell 10 x end cell row blank equals cell 10 open parentheses 5 over 12 square root of 6 close parentheses end cell row blank equals cell 25 over 6 square root of 6 end cell end table

Sehingga diperoleh nilai tan space C, yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell tan space straight C end cell equals cell AD over CD end cell row blank equals cell fraction numerator 10 over denominator begin display style 5 over 6 end style square root of 6 end fraction end cell row blank equals cell 10 times fraction numerator 6 over denominator 5 square root of 6 end fraction end cell row blank equals cell fraction numerator 60 over denominator 5 square root of 6 end fraction end cell row blank equals cell fraction numerator 12 over denominator square root of 6 end fraction times fraction numerator square root of 6 over denominator square root of 6 end fraction end cell row blank equals cell 12 over 6 square root of 6 end cell row blank equals cell 2 square root of 6 end cell end table

Dengan demikian, nilai tan space C adalah 2 square root of 6.

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