Cosines law, 2x

Boss

Looking for solutions of these two

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Prove It

MHF Helper
In the second, use the Sine Rule to evaluate angle B. This will be enough information to get angle C. Then you can use the Sine Rule to evaluate AB.

skeeter

MHF Helper
For the 1st problem ... AO, BO, and CO (sketch it in) are all angle bisectors.

Angle BCO = 60 degrees, therefore angle OAB + angle OBA = 30 degrees $\implies$ angle AOB = 150 degrees

Use the cosine law with triangle AOB to determine AB

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Boss

Kudos guys, you are awesome.