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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

`45^(@)`

B

`60^(@)`

C

`75^(@)`

D

`90^(@)`

Text Solution

Verified by Experts

The correct Answer is:
c
Since , angles A,B and C are in AP
` :. 2B = A+C`
Also, `A+B+C=180^(@)`
` rArr 3B = 180^(@) rArr B = 60^(@)`

Using sine rule, we have
` a/(sinA)=b/(sinB)=c/(sinC)`
` rArr sin C = c/b sin B = (sqrt(2))/(sqrt(3)) sin 60^(@)`
` = (sqrt(2))/(sqrt(3))xx (sqrt(3))/2 = 1/(sqrt(2))= 45^(@)`
` rArr C 45^(@)`
` rArr A = 75^(@)` [ from Eqs. (i),(ii) and (iii)]
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