Jawaban:
3. <BAC = 180° - <ABC - <BCA
<BAC = 180° - 45° - 75°
<BAC = 60°
aturan sinus :
[tex] \frac{ac}{sin \: b} = \frac{bc}{ \sin \: a} \\ \frac{ac}{ \sin(45) } = \frac{6}{ \sin(60) } \\ \frac{ac}{ \frac{ \sqrt{2} }{2} } = \frac{6}{ \frac{ \sqrt{3} }{2} } \\ \frac{ \sqrt{3} }{2} \times ac = 3 \sqrt{2} \\ ac = 3 \sqrt{2} \times \frac{2}{ \sqrt{3} } \\ ac = \frac{6 \sqrt{2} }{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } \\ ac = 2 \sqrt{6} [/tex]
4. aturan cosinus:
[tex] {a}^{2} = {b}^{2} + {c}^{2} - 2bc \cos(a) \\ {a}^{2} = {6}^{2} + {8}^{2} - 2 \: . \: 6 \: . \: 8 \: . \: \cos(60) \\ {a}^{2} = 36 + 64 - 96 \: . \: \frac{1}{2} \\ {a}^{2} = 100 - 48 \\ {a}^{2} = 52 \\ a = \sqrt{52} \\ a = 2 \sqrt{13} [/tex]
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