In a ∆ABC, if a = 8, b = 9 and 3 cos C = 2, then C = ____________.

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Solution

a = 8 , b = 9
3 cosC = 2

⇒ cosC = $\frac{2}{3}$
also using, cosine formula

$\cos C = \frac{a^{2} + b^{2} - c^{2}}{2 a b} \Rightarrow \frac{2}{3} = \frac{8^{2} + 9^{2} - c^{2}}{2 \times 8 \times 9} \Rightarrow 4 \times 8 \times 3 = 8^{2} + 9^{2} - c^{2} \Rightarrow C^{2} = 8^{2} + 9^{2} - 12 \times 8 = 49 i . e C = 7$

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