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Angles A, B, C of a deltaABC are in AP ...

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

A

`30^(@)`

B

`15^(@)`

C

`75^(@)`

D

`45^(@)`

Text Solution

Verified by Experts

The correct Answer is:
C
Since , `B=(A+C)/(2)`
`rArrB=90^(@)-(B)/(2)rArrB=60^(@)[because A+B+C=180^(@)]`
`because(b)/(c)=(sqrt(3))/(sqrt(2))rArr(b)/(sqrt(3))=(c)/(sqrt(2))`
`therefore(sin60^(@))/(sqrt(3))=(sinC)/(sqrt(2))` " " [by sine rule]
`rArrsinC=(1)/(sqrt(2))rArrC=45^(@)`
`thereforeangleA=180^(@)-(60^(@)+45^(@))=75^(@)`
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