The angles A, B and C of a `Delta ABC` are in AP. If `b:c=sqrt(3):sqrt(2),` then `angle A` is equal to

Options

A. `30^(@)`
B. `15^(@)`
C. `75^(@)`
D. `45^(@)`

Answer

C

Explanation

Since, `B=(A+C)/(2)`
`rArr B=90^(@)-(B)/(2)`
`rArr B=60^(@) " " [therefore A+B+C=180^(@)]`
`therefore (sin60^(@))/(sqrt(3))=(sinC)/(sqrt(2))" " `[by sine rule]
`rArr sin C=(1)/(sqrt(2))`
`rArr C=45^(@)`
`therefore angle A=180^(@)-(60^(@)+45^(@))`
`angle A=75^(@)`