Pertanyaan

Diketahui △ A BC , titik D pada AC dengan AB = 8, BC = 10, AC = 12, dan BD = CD. Panjang AD = ....

Diketahui $△ A BC$ , titik D pada AC dengan AB = 8, BC = 10, AC = 12, dan BD = CD. Panjang AD = ....

A. Rizky

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

$Dengan space menggunakan space aturan space cosinus space pada space segitiga space ABC comma space maka cos space straight C equals fraction numerator AC squared plus BC squared minus AB squared over denominator 2. AC. BC end fraction cos space straight C equals fraction numerator AC squared plus BC squared minus AB squared over denominator 2. AC. BC end fraction cos space straight C equals fraction numerator 12 squared plus 10 squared minus 8 squared over denominator 2.12.10 end fraction cos space straight C equals fraction numerator 144 plus 100 minus 64 over denominator 240 end fraction cos space straight C equals 180 over 240 box enclose cos space straight C equals 3 over 4 end enclose Pada space segitiga space BCD comma space maka cos space straight C equals fraction numerator CD squared plus BC squared minus BD squared over denominator 2. CD. BC end fraction 3 over 4 equals fraction numerator straight x squared plus 10 squared minus straight x squared over denominator 2. straight x.10 end fraction 3 over 4 equals fraction numerator 100 over denominator 20 straight x end fraction 3 over 4 equals 5 over straight x straight x equals fraction numerator 5.4 over denominator 3 end fraction box enclose straight x equals 20 over 3 end enclose Sehingga AD equals 12 minus straight x equals 12 minus 20 over 3 equals box enclose 16 over 3 end enclose$