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In a triangle ABC if 2a=sqrt(3)b+c, then...

In a triangle ABC if `2a=sqrt(3)b+c`, then possible relation is

A

`c^(2)=a^(2)+b^(2)-ab`

B

`a^(2)=b^(2)+c^(2)`

C

`b^(2)=a^(2)+c^(2)-ac sqrt(3)`

D

a = b = c

Text Solution

Verified by Experts

The correct Answer is:
B
`2a = sqrt(3b)+c`
`rarr a=(sqrt(3))/(2)b+(1)/(2)c`
`rArr sin A=(sqrt(3))/(2)sin B +(1)/(2)sin C`
`rArr cos S=(sqrt(3))/(2), cos B =(1)/(2)`
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