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The angles of DeltaABC are in A.P. If a:...

The angles of `DeltaABC` are in A.P. If `a:b=sqrt(2):sqrt(3)`, find the value of `angleA`.

Text Solution

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A,B,C are in A.P.
`rArr 2B=A+C`
but `A+B+C=180^(@)`
`rArr B+2B=180^(@)`
`B=60^(@)`
Now `a/(sinA)=b/(sinB)`
`rArr sinA=(asinB)/(b) = sqrt(2)/sqrt(3) xx sin60^(@)`
`=sqrt(2)/sqrt(3)xx sqrt(3)/ 2 = 1/sqrt(2)`
=`sin45^(2)`
`rArr A=45^(@)` Ans.
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