Pertanyaan

Diberikan segi-4 ABCD seperti pada gambar. Panjang CD adalah ....

cm
13 cm
12 cm
cm
cm

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F. Kurnia

Master Teacher

Mahasiswa/Alumni Universitas Jember

Jawaban terverifikasi

Pembahasan

$begin mathsize 14px style Perhatikan space segitiga space ADB comma space cari space panjang space BD space melalui space aturan space sinus fraction numerator BD over denominator sin invisible function application space straight A end fraction equals fraction numerator AD over denominator sin invisible function application space straight B end fraction fraction numerator BD over denominator sin invisible function application space 45 degree end fraction equals fraction numerator 10 over denominator sin space invisible function application 30 degree end fraction fraction numerator BD over denominator 1 half square root of 2 end fraction equals fraction numerator 10 over denominator 1 half end fraction BD equals 10 square root of 2 straight space cm Kemudian space perhatikan space segitiga space BCD space dan space melalui space aturan space cosinus space cari space CD comma CD squared equals BC squared plus BD squared minus 2 straight space BC. BD space cos invisible function application space straight B CD squared equals open parentheses 14 close parentheses squared plus open parentheses 10 square root of 2 close parentheses squared minus 2 open parentheses 14 close parentheses open parentheses 10 square root of 2 close parentheses space cos invisible function application space 45 degree CD squared equals 196 plus 200 minus 280 square root of 2 straight space open parentheses 1 half square root of 2 close parentheses CD squared equals 396 minus 280 CD equals square root of 116 CD equals 2 square root of 29 straight space cm end style$