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We have a triangle $ABC$ with $AB = 6.5$ , $BC=3.5$ and $AC = \sqrt{61}$. Can we calculate $\angle A$ using the law of cosines? I tried it but I kept getting wrong answers, so I'm wondering if it's possible?

I tried:


$(3.5)^2= (6.5)^2 + 61 -6.5\sqrt{61}\cos\gamma$

$91 = 6.5\sqrt{61}\cos\gamma$

$\cos\gamma = 1...$ which is impossible

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Of course it's possible. Show us your working, and we'll try to help. – TonyK Dec 16 '12 at 14:21
Can you use the second bullet ($\gamma$) with the graphic under Applications and follow the logic to find $\angle A$? – Amzoti Dec 16 '12 at 14:30
up vote 0 down vote accepted

You just forgot to multiply the term $ab\cos\gamma$ by $2$.

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