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Question

In a ΔABC, if   A=30 and b:c=2:3,findB.


Solution

Let B = 2k and c = 3k. Then,

cos A=b2+c2a22bc

cos 30=4k2+3k2a243k2

32×3k2=7k2a2

k2=a2k=a.

Thus,  b = 2a and c = 3a.

Now,  asinA=bsinBcsin30=2asinB

 sinB=(2a×12×1a)=1

B=90

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