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Perhatikan gambar berikut. Jika nilai  dan  tan. Panjang sisi  adalah...

Pertanyaan

Perhatikan gambar berikut.

Jika nilai cos alpha equals fraction numerator square root of 3 over denominator 2 end fraction dan tan beta equals 4 over 5 tan. Panjang sisi BC adalah...

  1. 5 square root of 3 space cm

  2. 4 square root of 3 space cm

  3. 3 square root of 3 cm

  4. 5 space cm

  5. 4 space cm

Pembahasan Soal:

Perhatikan segitiga siku-siku ABD. 

Diketahui cos alpha equals fraction numerator square root of 3 over denominator 2 end fraction, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space alpha end cell equals cell AB over BD end cell row cell fraction numerator square root of 3 over denominator 2 end fraction end cell equals cell 6 over BD end cell row BD equals cell fraction numerator 6 cross times 2 over denominator square root of 3 end fraction end cell row BD equals cell fraction numerator 12 over denominator square root of 3 end fraction cross times fraction numerator square root of 3 over denominator square root of 3 end fraction end cell row BD equals cell 4 square root of 3 space cm end cell end table 

Nilai dari tan beta equals 4 over 5, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell tan space beta end cell equals cell BD over BC end cell row cell 4 over 5 end cell equals cell fraction numerator 4 square root of 3 over denominator BC end fraction end cell row BC equals cell 5 over 4 cross times 4 square root of 3 end cell row BC equals cell 5 square root of 3 space cm end cell end table 

Jadi, jawaban yang tepat adalah A

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 15 Juni 2021

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