Cosine Rule , what good is it ?

AI Thread Summary
The discussion centers on the application of the Cosine Rule in problems involving vector quantities and negative lengths. It clarifies that while vector components can be negative, lengths themselves cannot be, as they are always non-negative. When using the Cosine Rule, only the magnitudes of the sides should be considered, not their directional components. For example, in a triangle with sides of -15 km and 10 km, one should use 15 km for calculations. The direction of the vectors is important, but it is addressed separately from the length calculations.
junior_J
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Cosine Rule , what good is it ?

Does the Cosine rule hold true for say negative lengths ? as in a vector quantity like displacement ?

I came across this problem which had -15km and 10km as the known sides whereas the angle opposite the unkown side is 60 degree ...

I tries using c^2 = a^2 + b^2 - 2*a*b cosC but this didnt work ... then on account of frustration i forcibly changed the '-' part of the formula to a '+' only to find that it works ... ?

Can someone explain this to me ??
 
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ther is no such thing as negative lenght, there is negative coordinates since somepoint has to be 0 and one side will be posetive and the other negative
 
the 60 degrees is negative, because it is east of north.
 
negative displacement ? would that apply to the cosine rule ?
 
There is no such thing as a negative length. A vector quantity (say, in a one-dimensional problem on a number line), or the components of the vector might be negative but the length is always non-negative. If you are using the cosine law in a vector problem, use the lengths, not the components.
 
so if i had a velocity oh say -15 km/hr ... id use 15 instead of -15 ?? as one of the sides of a triangle ?
 
yes you would, because you only care about magnitude. The direction comes later.
 

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