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If in triangle ABC, (a=(1+sqrt(3))c m ,b...

If in triangle ABC, `(a=(1+sqrt(3))c m ,b=2c m ,a n d/_C=60^0` , then find the other two angles and the third side.

Text Solution

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From `cos C = (a^(2) + b^(2) - c^(2))/(2ab)`, we have
`(1)/(2) = ((1 + sqrt3)^(2) + 4 -c^(2))/(2(1 + sqrt3) 2)`
or `2 + 2sqrt3 = 1+ 3 + 2sqrt3 + 4 - c^(2)`
or `c^(2) = 6 " or " c = sqrt6 cm`
Also, `(sin A)/(a) = (sin B)/(b) = (sin C)/(c)`
or `(sin A)/(1 + sqrt3) = (sin B)/(2) = (sqrt3//2)/(sqrt6)`
`rArr sin B = (1)/(sqrt2) " or " B = 45^(@)`
and `A = 180^(@) - (60^(@) + 45^(@)) = 75^(@)`
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