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In a DeltaABC, if A=45^(@) and B=75^(@),...

In a `DeltaABC`, if `A=45^(@)` and `B=75^(@)`, then `a+sqrt(2)c=`

A

b

B

2b

C

3b

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
We have,
`A=45^(@) and B=75^(@)`
`impliesC=180^(@)-(A+B)=180^(@)-120^(@)=60^(@)`
Now, `(a)/(sinA)=(b)/(sinB)=(c)/(sinC)`
`(a)/(sin45^(@))=(b)/(sin75^(@))=(c)/(sin60^(@))`
`implies(a)/(1//sqrt(2))=(b)/((sqrt(3)+1)/(2sqrt(2)))=(c)/(sqrt(3)//2)`
`impliesa-(2b)/(sqrt(3)+1)and c=(sqrt(6)b)/(sqrt(3)+1)`
`implies a+sqrt(2)c=(2b)/(sqrt(3)+1)+(2sqrt(3)b)/(sqrt(3)+1)=2b`
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