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Trigonometri
- Aturan Cosinus

AC = b = ¹⁰/₃√3 cm
BC = a = 10 cm
∠BAC = ∠A = 60°

∠C = __ ?

Aturan Cosinus :
a² = b² + c² - 2bc cos A
10² = (¹⁰/₃√3)² + c² - (2 × ¹⁰/₃√3 × c × cos 60°)
[tex] \frac{200}{3} = c^2 - \frac{10}{3} \sqrt3 \ c \ [\times \ 3] [/tex]
200 = c² - 10√3 c
3c² - 10√3 c - 200 = 0

a = 3 , b = - 10√3 , c = -200

D = b² - 4ac
D = (-10√3)² - 4(3)(-200)
D = 2700
√D = √2700
√D = 30√3

[tex] c_{1,2} = \frac{-b \pm \sqrt{D}}{2a} \\
c_{1,2} = \frac{10 \sqrt3 \pm 30 \sqrt{3}}{6} \\
Nilai \ yg \ memenuhi \ hanya \\
= \frac{10 \sqrt3 + 30 \sqrt{3}}{6} \\
= \frac{40 \sqrt{3}}{6} \\
= \frac{20 \sqrt{3}}{3} \ cm[/tex]

Maka :
[tex] \cos C = \frac{a^2 + b^2 - c^2}{2ab} \\
\cos C = \frac{10^2 + ( \frac{10 \sqrt{3}}{3})^2 - (\frac {20 \sqrt{3}}{3})^2}{2 \cdot 10 \cdot \frac{10 \sqrt{3}}{3}} \\
\cos C = 0 [/tex]
∠C = 90°

[B]