Trignometry Proof Help: Angle A < 60 Degrees

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Trignometry Proof Help!

If a,b,c are sides in a triangle such that a<1/2(b+c) show that angle A (the angle opposite to side a) is less than 60 degrees
 
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Have you tried the law of cosines?

a2=b2+c2-2bccosA
 

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