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Perhatikan gambar berikut!     Hitunglah panjang CD, AC, AD, BD, dan AB!

Pertanyaan

Perhatikan gambar berikut!
 


 

Hitunglah panjang CDACADBD, dan AB!

Y. Fathoni

Master Teacher

Mahasiswa/Alumni Universitas Negeri Yogyakarta.

Jawaban terverifikasi

Jawaban

diperoleh panjang CDACADBD, dan AB berturut-turut adalah 18 space cm18 square root of 3 space cm36 space cm18 square root of 2 space cm, dan open parentheses 18 square root of 3 minus 18 close parentheses space cm.

Pembahasan

Gunakan konsep sudut istimewa trigonometri dan perbandingan sisi trigonometri.

table attributes columnalign right center left columnspacing 2px end attributes row cell sin space alpha end cell equals cell fraction numerator sisi space depan space alpha over denominator sisi space miring end fraction end cell row cell tan space alpha end cell equals cell fraction numerator sisi space depan space alpha over denominator sisi space samping space alpha end fraction end cell row cell tan space 30 degree end cell equals cell 1 third square root of 3 end cell row cell tan space 45 degree end cell equals 1 row cell sin space 30 degree end cell equals cell 1 half end cell row cell sin space 45 degree end cell equals cell 1 half square root of 2 end cell end table

*Menentukan panjang CD.

table attributes columnalign right center left columnspacing 2px end attributes row cell tan space 45 degree end cell equals cell fraction numerator sisi space depan space 45 degree over denominator sisi space damping space 45 degree end fraction end cell row 1 equals cell CD over BC end cell row 1 equals cell CD over 18 end cell row CD equals cell 18 space cm end cell end table

*Menentukan panjang AC.

table attributes columnalign right center left columnspacing 2px end attributes row cell tan space 30 degree end cell equals cell fraction numerator sisi space depan space 30 degree over denominator sisi space damping space 30 degree end fraction end cell row cell 1 third square root of 3 end cell equals cell CD over AC end cell row cell 1 third square root of 3 end cell equals cell 18 over AC end cell row AC equals cell fraction numerator 18 over denominator begin display style 1 third end style square root of 3 end fraction end cell row AC equals cell fraction numerator 18 over denominator begin display style fraction numerator square root of 3 over denominator 3 end fraction end style end fraction end cell row AC equals cell 18 cross times fraction numerator 3 over denominator square root of 3 end fraction end cell row AC equals cell fraction numerator 54 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 AC equals cell 54 over 3 square root of 3 end cell row AC equals cell 18 square root of 3 space cm end cell end table

*Menentukan panjang AD.

table attributes columnalign right center left columnspacing 2px end attributes row cell sin space 30 degree end cell equals cell fraction numerator sisi space depan space 30 degree over denominator sisi space miring end fraction end cell row cell 1 half end cell equals cell CD over AD end cell row cell 1 half end cell equals cell 18 over AD end cell row cell AD cross times 1 end cell equals cell 18 cross times 2 end cell row AD equals cell 36 space cm end cell end table

*Menentukan panjang BD.

table attributes columnalign right center left columnspacing 2px end attributes row cell sin space 45 degree end cell equals cell fraction numerator sisi space depan space 45 degree over denominator sisi space miring end fraction end cell row cell 1 half square root of 2 end cell equals cell CD over BD end cell row cell 1 half square root of 2 end cell equals cell 18 over BD end cell row BD equals cell fraction numerator 18 over denominator begin display style 1 half end style square root of 2 end fraction end cell row BD equals cell fraction numerator 18 over denominator begin display style fraction numerator square root of 2 over denominator 2 end fraction end style end fraction end cell row BD equals cell 18 cross times fraction numerator 2 over denominator square root of 2 end fraction end cell row BD equals cell fraction numerator 36 over denominator square root of 2 end fraction cross times fraction numerator square root of 2 over denominator square root of 2 end fraction end cell row BD equals cell 36 over 2 square root of 2 end cell row BD equals cell 18 square root of 2 space cm end cell end table

*Menemukan panjang AB.

table attributes columnalign right center left columnspacing 2px end attributes row AC equals cell AB plus BC end cell row cell 18 square root of 3 end cell equals cell AB plus 18 end cell row AB equals cell open parentheses 18 square root of 3 minus 18 close parentheses space cm end cell end table

Jadi, diperoleh panjang CDACADBD, dan AB berturut-turut adalah 18 space cm18 square root of 3 space cm36 space cm18 square root of 2 space cm, dan open parentheses 18 square root of 3 minus 18 close parentheses space cm.

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