Hitunglah panjang CD, AC, AD, BD, dan AB!

Pertanyaan

Hitunglah panjang CD, AC, AD, BD, dan AB!

S. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. DR. Hamka

Jawaban terverifikasi

Pembahasan

Ingatlah bahwa:

tan space alpha equals depan over samping

Sehingga diperoleh:

  • Panjang CD

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 60 degree end cell equals cell fraction numerator CD over denominator 12 space cm end fraction end cell row cell square root of 3 end cell equals cell fraction numerator CD over denominator 12 space cm end fraction end cell row CD equals cell 12 square root of 3 space cm end cell end table

  • Panjang AC

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 12 square root of 3 space cm over denominator AC end fraction end cell row cell 1 third square root of 3 end cell equals cell fraction numerator 12 square root of 3 space cm over denominator AC end fraction end cell row AC equals cell fraction numerator 12 square root of 3 space cm over denominator begin display style 1 third end style square root of 3 end fraction end cell row AC equals cell 12 down diagonal strike square root of 3 end strike space cm cross times fraction numerator 3 over denominator down diagonal strike square root of 3 end strike end fraction end cell row AC equals cell 36 space cm end cell end table

Kemudian dengan menggunakan Teorema Pytahgoras, diperoleh:

  • Panjang AD

table attributes columnalign right center left columnspacing 0px end attributes row cell AD squared end cell equals cell AC squared plus CD squared end cell row AD equals cell plus-or-minus square root of AC squared plus CD squared end root end cell row AD equals cell plus-or-minus square root of open parentheses 36 space cm close parentheses squared plus open parentheses 12 square root of 3 space cm close parentheses squared end root end cell row AD equals cell plus-or-minus square root of 1.296 space cm squared plus 432 space cm squared end root end cell row AD equals cell plus-or-minus square root of 1.728 space cm squared end root end cell row AD equals cell plus-or-minus 24 square root of 3 space cm end cell row AD equals cell 24 square root of 3 space cm end cell end table

  • Panjang BD

table attributes columnalign right center left columnspacing 0px end attributes row cell BD squared end cell equals cell BC squared plus CD squared end cell row BD equals cell plus-or-minus square root of BC squared plus CD squared end root end cell row BD equals cell plus-or-minus square root of open parentheses 12 space cm close parentheses squared plus open parentheses 12 square root of 3 space cm close parentheses squared end root end cell row BD equals cell plus-or-minus square root of 144 space cm squared plus 432 space cm squared end root end cell row BD equals cell plus-or-minus square root of 576 space cm squared end root end cell row BD equals cell plus-or-minus 24 space cm end cell row BD equals cell 24 space cm end cell end table

  • Panjang AB

table attributes columnalign right center left columnspacing 0px end attributes row AB equals cell AC minus BC end cell row blank equals cell 36 space cm minus 12 space cm end cell row blank equals cell 24 space cm end cell end table

Maka, panjang CD, AC, AD, BD, dan AB adalah 12 square root of 3 space cm36 space cm24 square root of 3 space cm24 space cm, dan 24 space cm.

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