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In a triangle ABC, if (sqrt3-1)a = 2b,...

In a triangle ABC, if `(sqrt3-1)a = 2b, A = 3B`, then `/_C` is

A

`60^(@)`

B

`120^(@)`

C

`30^(@)`

D

`45^(@)`

Text Solution

Verified by Experts

The correct Answer is:
B
Since , `(a)/(b)=(2)/(sqrt(3)-1)andA=3B`
By sine rule , `(sinA)/(sinB)=(a)/(b)rArr(sin3B)/(sinB)=(2)/(sqrt(3)-1)`
`rArr(3sinB-4sin^(3)B)/(sinB)=(2)/(sqrt(3)-1)`
`rArr(2-sqrt(3))/(4)=sin^(2)B`
`rArr(4-2sqrt(3))/(8)=sin^(2)B`
`rArr((sqrt(3)-1)^(2))/(8)=sin^(2)B`
`rArrsinB=(sqrt(3)-1)/(2sqrt(2))`
`rArrangleB=15^(@),angleA=45^(@)andangleC=120^(@)`
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