Diketahui segitiga ABC siku-siku di B . jika
Matematika
fira899
Pertanyaan
Diketahui segitiga ABC siku-siku di B . jika <A = 30° dan AC = 18 cm , hitunglah : a. panjang AB dan BC . b. sin <C , cos <C, dan tan <C
1 Jawaban
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1. Jawaban adhikagni
a.
[tex] \cos(30) = \frac{ab}{18} \\ \frac{1}{2} \sqrt{3} = \frac{ab}{18} \\ ab = 9 \sqrt{3 } \: cm[/tex]
[tex] \sin(30) = \frac{bc}{18} \\ \frac{1}{2} = \frac{bc}{18} \\ 2bc = 18 \\ bc = 9 \: cm[/tex]
b. <C = 180 - (90 + 30)
=180 - 120
= 60°
[tex] \sin(60) = \frac{9 \sqrt{3} }{18} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{2} \sqrt{3} [/tex]
[tex] \cos(60) = \frac{9}{18} = \frac{1}{2} [/tex]
[tex] \tan(60) = \frac{9 \sqrt{3} }{9} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \sqrt{3} [/tex]