If in a `DeltaABC,A=30^(@),B=45^(@)` and a = 1, then the values of b and c are respectively

Options

A. `sqrt(2),(sqrt(3)+1)/(sqrt(2))`
B. `sqrt(2),(sqrt(3)-1)/(sqrt(2))`
C. `sqrt(3),(sqrt(3)-1)/(sqrt(2))`
D. `sqrt(2),(sqrt(3)+2)/(sqrt(2))`

Answer

A

Explanation

Given, `A=30^(@),B=45^(@),a=1`
Using sine rule,
`(a)/(sinA)=(b)/(sinB)=(c)/(sinC)`
`implies(1)/(((1)/(2)))=(b)/(((1)/(sqrt(2))))=(c)/(sin.105^(@))`
`impliesb=sqrt(2)andc=2sin105^(@)`
`therefore c=2((sqrt(3)+1)/(2sqrt(2)))=(sqrt(3)+1)/(sqrt(2))`