What is the difference between the two sine rules for resultant vector?

[eben]

Hello can anyone help me with this:

there are two sine rules for finding the direction of a resultant vector;one for the sides and one for the angle;

I tested both formulas and they all worked well and gave me equal answers, does that mean I can use them interchangeably,the rules are:
a/sinA = b/sinB=c/sinC(for finding the sides) and

sinA/a=sinB/b=sinC/c(for finding the angles)

 

[andrewkirk]

There is only one rule. The second one you wrote is just what you get when you take the reciprocals of all the items. Naturally if a=b and neither a nor b is zero then it will also be true that 1/a = 1/b. Whenever you perform the same operation on both sides of the equation, the equality still holds, as long as the operation hasn't produced an error (eg divide by zero)
So yes, you can use either of the two versions that you wrote above.

 

[eben]

thanks very much,God bless you.

 

[jedishrfu]

One way to prove its true:

$x=y$ with neither x nor y equal to 0

mpy both sides by $1/x$: . . . . . . . . $1 = y/x$

mpy both sides by $1/y$: . . . . . . . . $1/y = 1/x$

Hence: $1/x = 1/y$

 

[Gavran]

There are four rules and they are the law of sines, the law of cosines, the law of tangents and the law of cotangents. The law of sines and the law of cosines are more common than the law of tangents and the law of cotangents.

The law of sines and the law of cosines can be used for finding a resultant vector or more commonly for finding lengths and angles in scalene triangles and there is a difference between the law of sines and the law of cosines.