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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

Text Solution

Verified by Experts

The correct Answer is:
`120^(@)`
We have `(sqrt3 -1) a = 2b`
`rArr (a)/(2) = (b)/(sqrt3 -1)`
`rArr (sin A)/(2) = (sin B)/(sqrt3 -1)`
`rArr (sin 3B)/(2) = (sin B)/(sqrt3 -1)`
`rArr 3 - 4 sin^(2) B = (2)/(sqrt3 -1)`
`rArr 3 - 4 sin^(2) B = sqrt3 + 1`
`rArr sin^(2) B = (2- sqrt3)/(4)`
`rArr sin^(2) B = ((sqrt3 -1)^(2))/(8)`
`rArr sin B = +- (sqrt3 -1)/(2sqrt2)`
`rArr sin B = (sqrt3 -1)/(2 sqrt2)` (as sin B is positive)
Thus, `B = 15^(@), A = 45^(@) and C = 120^(@)`
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