Question

Which of the following cannot be derived from the law of sines?

A.) b/sinB=sinA/a

B.) a*sinB=b*sinA

C.) sinC/sinA=c/a

D.) c*sinA=a*sinC

Answer 1

A.) b/sinB=sinA/a. hope it helps

Answer 2

`(b)/(SinB)=(SinA)/(a)`

Explanation:

Sine Rule =
`(Sin A)/(a) =(Sin B)/(b)=(Sin C)/(c)`

a)
`(b)/(SinB)=(SinA)/(a)`

Sine rule is
`(Sin A)/(a) =(Sin B)/(b)`

`(b)/(Sin B) =(a)/(Sin A)`

Thus Option 1 cannot be derived from the law of sines

b)
`a* sinB=b* sinA`

Sine rule is
`(Sin A)/(a) =(Sin B)/(b)`

`(b)/(Sin A) =(a)/(Sin B)`

Thus Option B can be derived from the law of sines.

c)
`(Sin C)/(SinA)=(c)/(a)`

Sine rule is
`(Sin A)/(a) =(Sin C)/(c)`

`(c)/(a) =(SinC)/(Sin A)`

Thus Option C can be derived from the law of sines.

d)
`c * sinA=a* sinC`

Sine rule is
`(Sin A)/(a) =(Sin C)/(c)`

`c * sinA=a* sinC`

Thus Option C can be derived from the law of sines.

Hence Option A cannot be derived from the law of sines

`(b)/(SinB)=(SinA)/(a)`