Angles A, B, C of a `deltaABC` are in AP and `b : c = sqrt3 : sqrt2`, then `/_A` is given by

Options

A. `75^(@)`
B. `45^(@)`
C. `60^(@)`
D. None of these

Answer

A

Explanation

`because A+C=2B`
`thereforeA+B+C=3B=180^(@)`
`thereforeB=60^(@)`
`thereforeA+C=120^(@)`
Now `b:c=sqrt(3):sqrt(2)`
`thereforesinB:sinC=sqrt(3):sqrt(2)`
`thereforesinC=(sqrt(2))/(sqrt(3))sinB=(sqrt(2))/(sqrt(3))sin60^(@)`
`=(sqrt(2))/(sqrt(3))*(sqrt(3))/(2)=(1)/(sqrt(2))`
`impliesC=45^(@)`
`thereforeA=180^(@)-(60^(@)+45^(@))=75^(@)`