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Pada trapesium ABCD, DA ⊥ AB dan sisi AB > DC. Dari titik C ditarik garis AD memotong AB di titik E. Jika diketahui begin mathsize 14px style angle end styleABD = 20°, begin mathsize 14px style angle end styleDBC = 40°, DC = 10 satuan, maka panjang sisi BC adalah ...

  1. begin mathsize 14px style 5 over 2 sin space 20 degree end style

  2. 5 sec 20°

  3. begin mathsize 14px style 5 over 2 sec space 40 degree end style

  4. 5 cos 40°

  5. 5 tan 20°

A. Rizky

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

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Pembahasan

begin mathsize 14px style Segitiga space FEB space sebangun space dengan space segitiga space CFD comma space akibatnya space  angle CDF equals angle FBE equals 20 degree.  Misalkan space panjang space BE equals straight x. space Dengan space perbandingan space tangen space  diperoleh  tan space 20 degree equals FE over BE equals FE over straight x rightwards double arrow FE equals straight x space tan space 20 degree space dan  tan space 20 degree equals CF over CD equals CF over 10 rightwards double arrow CF equals 10 space tan space 20 degree space dan  tan space 60 degree equals CE over BE rightwards double arrow square root of 3 equals CE over straight x rightwards double arrow CE equals straight x square root of 3    Karena space CE space equals space CF space plus space FE space maka  rightwards double arrow straight x square root of 3 equals 10 space tan space 20 degree plus straight x space tan space 20 degree  rightwards double arrow straight x square root of 3 minus straight x space tan space 20 degree equals 10 space tan space 20 degree  rightwards double arrow straight x left parenthesis square root of 3 minus tan space 20 degree right parenthesis equals 10 space tan space 20 degree  rightwards double arrow straight x equals fraction numerator 10 space tan space 20 degree over denominator square root of 3 minus tan space 20 degree end fraction    Dengan space rumus space pythagoras space diperoleh  BC equals square root of BE squared plus CE squared end root  BC equals square root of straight x squared plus open parentheses straight x square root of 3 close parentheses squared end root  BC equals square root of straight x squared plus 3 straight x squared end root  BC equals square root of 4 straight x squared end root  BC equals 2 straight x  BC equals 2 open parentheses fraction numerator 10 space tan space 20 degree space over denominator square root of 3 minus tan space 20 degree end fraction close parentheses  BC equals fraction numerator 20 space tan space 20 degree over denominator square root of 3 minus tan space 20 degree end fraction  BC equals fraction numerator 20 space tan space 20 degree over denominator square root of 3 minus tan space 20 degree end fraction cross times fraction numerator cos space 20 degree over denominator cos space 20 degree end fraction  BC equals fraction numerator 20 space sin space 20 degree over denominator square root of 3 space cos space 20 degree minus sin space 20 degree end fraction  BC equals fraction numerator 20 space sin space 20 degree over denominator 2 open parentheses 1 half square root of 3 space cos space 20 degree minus 1 half sin space 20 degree close parentheses end fraction  BC equals fraction numerator 20 space sin space 20 degree over denominator 2 open parentheses sin space 60 degree space cos space 20 degree minus cos space 60 degree space sin space 20 degree close parentheses end fraction  BC equals fraction numerator 20 space sin space 20 degree over denominator 2 space sin space left parenthesis 60 degree minus 20 degree right parenthesis end fraction  BC equals fraction numerator 20 space sin space 20 degree over denominator 2 space sin space 40 degree end fraction  BC equals fraction numerator 20 space sin space 20 degree over denominator 4 space sin space 20 degree space cos space 20 degree end fraction  BC equals fraction numerator 5 over denominator cos space 20 degree end fraction  BC equals 5 space sec space 20 degree end style

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