If a : b : c = 4 : 5 : 6, then show that $∠ C = 2 ∠ A .$

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Solution

$a : b : c = 4 : 5 : 6$
$c o s A = \frac{b^{2} + c^{2} + a^{2}}{2 b c} = \frac{5^{2} + 6^{2} - 4^{2}}{2 \times 5 \times 6} = \frac{3}{4} \Rightarrow A = 41^{\circ} 41^{\circ}$
$c o s C = \frac{a^{2} + b^{2} - c^{2}}{2 a b} = \frac{4^{2} + 5^{2} - 6^{2}}{2 \times 4 \times 5} = \frac{1}{8} \Rightarrow C = 82.32$
$∠ C = 2 ∠ A$ HP

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