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Question
The angles of the ΔABC are in A.P. and b:c=`sqrt3:sqrt2` then find`angleA,angleB,angleC`
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Solution
`angleA, angleB, angleC` are in A.P and `b:c=sqrt3:sqrt2`
`therefore 2B=A+C`
`2B=180^@-B` ...............[`because A+B+C=180^@`]
`3B=180^@`
`angleB=60^@`
In ΔABC by sine rule, we have
`sinB/b=sinC/c`
`sinB/sinC=b/c`
`sin60^@/sinc=sqrt3/sqrt2`
`sqrt3/2=sqrt3/sqrt2=sinC`
`sinC=1/sqrt2`
`angle C=45^@`
`angleA=180^@-60^@-45^@=75^@`
Thus, the angles of ΔABC are `angleA=75^@,angleB=60^@,angleC=45^@`
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