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.

Options

A. `45^(@) and 75^(@)`
B. `30^(@) and 90^(@)`
C. `105^(@) and 15^(@)`
D. `100^(@) and 20^(@)`

Answer

A

Explanation

Now as a `gt` b
`therefore angle A gt angle B`
Now from Sine Rule, `(sinA)/(a)=(sinB)/(b)`
`(sinA)/(1+sqrt(3))=(sinB)/(2)`
From option (a), `(sin 75)/(1+sqrt(3))=(sin 45)/(2)`
`(sqrt(6)+sqrt(2))/(4(1+sqrt(3)))=(1)/(2sqrt(2))`
`2sqrt(12)+4=4+4sqrt(3)`
`4+4 sqrt(3) = 4 + sqrt(3)`
`therefore` Option (a) is correct.